Apostila de calculo III 1990 II

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Apostila de calculo III 1990 II

Transcript of Apostila de calculo III 1990 II

Page 1: Apostila de calculo  III 1990 II

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Page 2: Apostila de calculo  III 1990 II

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COiYQ2 de ltjoh _lo -Q6~do do ~~~ (~i~~o) de Gl-iec

~()lQ lJ1(tJl Jtl) d)uacuteNaacute~ ot Q ()l~ tHJ tMampuoiNeuro QIw ~ t~a~tio de ~ r~ o ~ -UD

P () p t ()1)) 3 D~ YID uacute) TltQ)-- t(o) bl-a)+- -t(o) lt-o) ~ i-Ia) (~-Q) + t- 1- lo) lJ- 0)1- R

1f 2~ ~ hf pM+t) ~-I-i

o~ ~h +LQte(te-o)1 1t--) 0lt eI lti (7)( (-+i) w

~uumld -= ~ + ~lJ L1i-a) -t el~~) llf-J+ f~L~-Or+ 1 ~) dT

~~) lI( - Q) -l- J-= t- - l_~ tooo I04

OotY ~ Il0-0 -1MC _ 1lt- c

~ER~ QE -~1Or ~e ~) ~~ -=~lt)W d~ ~IC) ~ ~ne tk lCli0 ~l f -Ccedilk) ~ I~ Q J lt ~

~b ~ o~ o) QouJ~~

Je

Wl~ f ~) -4~ lJlt Ilt -

ccgt n ~ ~ (

10

U4)odo ~II (n+i) V 1

Vl~ n(

li

-

~lt ~ ~iJ~ ~ MPc~ C-UM~ ~~) l~1clt MIacutegtie

I()~)~ ~ ) ~ lo) IJQM 10

) f(~) ((Ol ~ ) f lo) Cco o r 1shy

~ )

tt) - 1)Qv)( -+-lo) - IRN o o

fl)

~) _CoDt( tlto) ~ - cooo =- -1 ~ ) i

cshy-+ (t) ~ -(-DeuJ( J +lQ) ~o O

rt LV +4 (-1) 1(

~+~)

~h-igt Qn = --1--shy

(~n-~) ~ l H-il

L+i ~ l- i) ~

(Llni-t)-d ~

n-j)-1 ~~ thf

n ltgtOacute ~Y-) QM - I trM ~~uacute ltt- -1-) tl-cgtooS

i ~+~ lih-i) ~

~-i) lth4L)~ ( Lt -+- t) ~

Q~ ~IW ( 4~~ RV ) c 1 cgt6 h-tgt06

~V7 OJ J~ ~lt

460~JD ~d J)Q ~ ~I ~~ YltJiO ~

U~ f1W d(Sta ~

VY~3W~

~~~~~~~tt~) ~~Th

i 2 4 I bullbullbullbull YL) bull ~31

-o

(lt ~ QVt- ~Vl euro J

i~ e 2 3gt 4 J bull bullbull J

at~ Q~l

l413~~H)O )

shy5ERlES

Ml~ CJo ~~do tk J)QJv~do o ~1fr1 Vi

~O

o) ~ b A ~ b ~1 ~~ ~oo)e bW- ~Q~ euro ~ Golf() ~ 11middot b

00

~amp ~oA - i1I~v1 ~ ~oo-~ ~~ ( c) COlt ~tft Agrave mOO WfAtildeDIi I ~ JJQJl p~~ ocirce o li tQ~ i

1t~Mgt 1 ~

- --------- -~--__-------------- shy

reg r ~~ch~ 2 ~ n~~

yt i Y~ e

5 lt )(~N~t~~middotmiddot~~middot ~ llW (~IV3 ) = - 06 t+=gtoacute Q-+ ~

~n ~ t ~ltPBA 1 ~

~~ ~ -OeacuteJJlt

l -i ~~

o) ~l L1

b) l~ 1

t) tl i

~BmiddotO

~i ~Dgt 6c-

~ li-t ) ( i - i) ~ ( r) t + ( ~ - -tJ I)n ~ (i - L )

ttTi

~W ~ ~1Yf l - L ) = 1 ~ 1lt nlto( --o n+

~

middotr

2 3 ~ 12 ~ L 3 1

I 5) 1-) ~1) J

2) t~-l)~ ~jl -i i)-i~ middot t-~)t middot3

Jl

1I~middot ~h ~ --ltI

~ 3 4J - - --I ~+-t - 3 5 l l ~ ehn --I I 11~

deg1 52-+L ~ Iz

reg

SEQJE-NCAS

~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

- Q ~~IY lo l1eacute lO ~Jshy~~~~=~ ~~t=~ -ltot YI ~) U IYV euro

~ L~t ~ J bullbullbull I

0)

-i~ Ilt ~ d

~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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Page 3: Apostila de calculo  III 1990 II

r -__--

T$ bull A~(L ~ ) bullnd t lVt) li V+

Cgtoacute

Z ~n~ Jh ~ tv (l )VI +1Yt=1 V+z

-agrave ~_j Y)

h~ -t ~ 1-1shyi-~

CruT~oamp Pt-AA ~W~Mgt no ~A Con Araquof~~) lgte Jf sr ~ie __

~e ~Ni~~ b~ ~ ~Titraquo 1R~IIN~ a ~~Q e ~Ot ~ ~

ou ~~

~ ~atilde1I0 ~~ ll020I1~) g ~ (t MIYVA li~ CfJ1IMlJCi) ~ ~tyy()Q PI1A (t1Ob--J f-1 ~l

Qeacute C) gteacute4 CAgtr-IL~ Ae1f ij Q7l o 4i~e ck~e

~ 1 - fullo () wkY~o (VOJiQ IR chCid( Ilc~~ Cl ~~ ~ fle~(L

~ n+

QM ~Lp ~ n_ oQH) V4gtltgt06 ~middotHV

~w

-l

tyv ~ o L 1 ~4- J boacute~k~ lt L-tQ ~

bull

Z ~

rt i Vj

4vt ~~ shy

Qltshy

~--l~

~ ~ -=~YL k1N

(l~ 1 Q-t i ~

t~ Y+ 1shy

~~otgt

~

~+ ~ S 1 L

Q I)-euro-( ~~e

) shy leuro~ Ji e

COiYQ2 de ltjoh _lo -Q6~do do ~~~ (~i~~o) de Gl-iec

~()lQ lJ1(tJl Jtl) d)uacuteNaacute~ ot Q ()l~ tHJ tMampuoiNeuro QIw ~ t~a~tio de ~ r~ o ~ -UD

P () p t ()1)) 3 D~ YID uacute) TltQ)-- t(o) bl-a)+- -t(o) lt-o) ~ i-Ia) (~-Q) + t- 1- lo) lJ- 0)1- R

1f 2~ ~ hf pM+t) ~-I-i

o~ ~h +LQte(te-o)1 1t--) 0lt eI lti (7)( (-+i) w

~uumld -= ~ + ~lJ L1i-a) -t el~~) llf-J+ f~L~-Or+ 1 ~) dT

~~) lI( - Q) -l- J-= t- - l_~ tooo I04

OotY ~ Il0-0 -1MC _ 1lt- c

~ER~ QE -~1Or ~e ~) ~~ -=~lt)W d~ ~IC) ~ ~ne tk lCli0 ~l f -Ccedilk) ~ I~ Q J lt ~

~b ~ o~ o) QouJ~~

Je

Wl~ f ~) -4~ lJlt Ilt -

ccgt n ~ ~ (

10

U4)odo ~II (n+i) V 1

Vl~ n(

li

-

~lt ~ ~iJ~ ~ MPc~ C-UM~ ~~) l~1clt MIacutegtie

I()~)~ ~ ) ~ lo) IJQM 10

) f(~) ((Ol ~ ) f lo) Cco o r 1shy

~ )

tt) - 1)Qv)( -+-lo) - IRN o o

fl)

~) _CoDt( tlto) ~ - cooo =- -1 ~ ) i

cshy-+ (t) ~ -(-DeuJ( J +lQ) ~o O

rt LV +4 (-1) 1(

~+~)

~h-igt Qn = --1--shy

(~n-~) ~ l H-il

L+i ~ l- i) ~

(Llni-t)-d ~

n-j)-1 ~~ thf

n ltgtOacute ~Y-) QM - I trM ~~uacute ltt- -1-) tl-cgtooS

i ~+~ lih-i) ~

~-i) lth4L)~ ( Lt -+- t) ~

Q~ ~IW ( 4~~ RV ) c 1 cgt6 h-tgt06

~V7 OJ J~ ~lt

460~JD ~d J)Q ~ ~I ~~ YltJiO ~

U~ f1W d(Sta ~

VY~3W~

~~~~~~~tt~) ~~Th

i 2 4 I bullbullbullbull YL) bull ~31

-o

(lt ~ QVt- ~Vl euro J

i~ e 2 3gt 4 J bull bullbull J

at~ Q~l

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1t~Mgt 1 ~

- --------- -~--__-------------- shy

reg r ~~ch~ 2 ~ n~~

yt i Y~ e

5 lt )(~N~t~~middotmiddot~~middot ~ llW (~IV3 ) = - 06 t+=gtoacute Q-+ ~

~n ~ t ~ltPBA 1 ~

~~ ~ -OeacuteJJlt

l -i ~~

o) ~l L1

b) l~ 1

t) tl i

~BmiddotO

~i ~Dgt 6c-

~ li-t ) ( i - i) ~ ( r) t + ( ~ - -tJ I)n ~ (i - L )

ttTi

~W ~ ~1Yf l - L ) = 1 ~ 1lt nlto( --o n+

~

middotr

2 3 ~ 12 ~ L 3 1

I 5) 1-) ~1) J

2) t~-l)~ ~jl -i i)-i~ middot t-~)t middot3

Jl

1I~middot ~h ~ --ltI

~ 3 4J - - --I ~+-t - 3 5 l l ~ ehn --I I 11~

deg1 52-+L ~ Iz

reg

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~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

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~ L~t ~ J bullbullbull I

0)

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~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

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lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

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l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

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d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

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~ ~lt4QiIl

O~ ~~ ~~+

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el~ltJ lh~ ~=1)

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(ebou(f~ i-O)

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bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

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o

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~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

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~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

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Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

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~fo _fl__

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ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

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G~ocirc

Jk =-~

r

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oishy

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r (J

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~ ~ 6J - lJ

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secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

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lt5u ~J

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( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

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ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

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~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

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bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

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_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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Page 4: Apostila de calculo  III 1990 II

bull

Z ~

rt i Vj

4vt ~~ shy

Qltshy

~--l~

~ ~ -=~YL k1N

(l~ 1 Q-t i ~

t~ Y+ 1shy

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~

~+ ~ S 1 L

Q I)-euro-( ~~e

) shy leuro~ Ji e

COiYQ2 de ltjoh _lo -Q6~do do ~~~ (~i~~o) de Gl-iec

~()lQ lJ1(tJl Jtl) d)uacuteNaacute~ ot Q ()l~ tHJ tMampuoiNeuro QIw ~ t~a~tio de ~ r~ o ~ -UD

P () p t ()1)) 3 D~ YID uacute) TltQ)-- t(o) bl-a)+- -t(o) lt-o) ~ i-Ia) (~-Q) + t- 1- lo) lJ- 0)1- R

1f 2~ ~ hf pM+t) ~-I-i

o~ ~h +LQte(te-o)1 1t--) 0lt eI lti (7)( (-+i) w

~uumld -= ~ + ~lJ L1i-a) -t el~~) llf-J+ f~L~-Or+ 1 ~) dT

~~) lI( - Q) -l- J-= t- - l_~ tooo I04

OotY ~ Il0-0 -1MC _ 1lt- c

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~b ~ o~ o) QouJ~~

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10

U4)odo ~II (n+i) V 1

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li

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fl)

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cshy-+ (t) ~ -(-DeuJ( J +lQ) ~o O

rt LV +4 (-1) 1(

~+~)

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(~n-~) ~ l H-il

L+i ~ l- i) ~

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n-j)-1 ~~ thf

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i 2 4 I bullbullbullbull YL) bull ~31

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(lt ~ QVt- ~Vl euro J

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l413~~H)O )

shy5ERlES

Ml~ CJo ~~do tk J)QJv~do o ~1fr1 Vi

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o) ~ b A ~ b ~1 ~~ ~oo)e bW- ~Q~ euro ~ Golf() ~ 11middot b

00

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1t~Mgt 1 ~

- --------- -~--__-------------- shy

reg r ~~ch~ 2 ~ n~~

yt i Y~ e

5 lt )(~N~t~~middotmiddot~~middot ~ llW (~IV3 ) = - 06 t+=gtoacute Q-+ ~

~n ~ t ~ltPBA 1 ~

~~ ~ -OeacuteJJlt

l -i ~~

o) ~l L1

b) l~ 1

t) tl i

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~i ~Dgt 6c-

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~

middotr

2 3 ~ 12 ~ L 3 1

I 5) 1-) ~1) J

2) t~-l)~ ~jl -i i)-i~ middot t-~)t middot3

Jl

1I~middot ~h ~ --ltI

~ 3 4J - - --I ~+-t - 3 5 l l ~ ehn --I I 11~

deg1 52-+L ~ Iz

reg

SEQJE-NCAS

~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

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~Qocirc i~~q

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= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

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b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

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Z

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-1 1

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l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

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~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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Page 5: Apostila de calculo  III 1990 II

COiYQ2 de ltjoh _lo -Q6~do do ~~~ (~i~~o) de Gl-iec

~()lQ lJ1(tJl Jtl) d)uacuteNaacute~ ot Q ()l~ tHJ tMampuoiNeuro QIw ~ t~a~tio de ~ r~ o ~ -UD

P () p t ()1)) 3 D~ YID uacute) TltQ)-- t(o) bl-a)+- -t(o) lt-o) ~ i-Ia) (~-Q) + t- 1- lo) lJ- 0)1- R

1f 2~ ~ hf pM+t) ~-I-i

o~ ~h +LQte(te-o)1 1t--) 0lt eI lti (7)( (-+i) w

~uumld -= ~ + ~lJ L1i-a) -t el~~) llf-J+ f~L~-Or+ 1 ~) dT

~~) lI( - Q) -l- J-= t- - l_~ tooo I04

OotY ~ Il0-0 -1MC _ 1lt- c

~ER~ QE -~1Or ~e ~) ~~ -=~lt)W d~ ~IC) ~ ~ne tk lCli0 ~l f -Ccedilk) ~ I~ Q J lt ~

~b ~ o~ o) QouJ~~

Je

Wl~ f ~) -4~ lJlt Ilt -

ccgt n ~ ~ (

10

U4)odo ~II (n+i) V 1

Vl~ n(

li

-

~lt ~ ~iJ~ ~ MPc~ C-UM~ ~~) l~1clt MIacutegtie

I()~)~ ~ ) ~ lo) IJQM 10

) f(~) ((Ol ~ ) f lo) Cco o r 1shy

~ )

tt) - 1)Qv)( -+-lo) - IRN o o

fl)

~) _CoDt( tlto) ~ - cooo =- -1 ~ ) i

cshy-+ (t) ~ -(-DeuJ( J +lQ) ~o O

rt LV +4 (-1) 1(

~+~)

~h-igt Qn = --1--shy

(~n-~) ~ l H-il

L+i ~ l- i) ~

(Llni-t)-d ~

n-j)-1 ~~ thf

n ltgtOacute ~Y-) QM - I trM ~~uacute ltt- -1-) tl-cgtooS

i ~+~ lih-i) ~

~-i) lth4L)~ ( Lt -+- t) ~

Q~ ~IW ( 4~~ RV ) c 1 cgt6 h-tgt06

~V7 OJ J~ ~lt

460~JD ~d J)Q ~ ~I ~~ YltJiO ~

U~ f1W d(Sta ~

VY~3W~

~~~~~~~tt~) ~~Th

i 2 4 I bullbullbullbull YL) bull ~31

-o

(lt ~ QVt- ~Vl euro J

i~ e 2 3gt 4 J bull bullbull J

at~ Q~l

l413~~H)O )

shy5ERlES

Ml~ CJo ~~do tk J)QJv~do o ~1fr1 Vi

~O

o) ~ b A ~ b ~1 ~~ ~oo)e bW- ~Q~ euro ~ Golf() ~ 11middot b

00

~amp ~oA - i1I~v1 ~ ~oo-~ ~~ ( c) COlt ~tft Agrave mOO WfAtildeDIi I ~ JJQJl p~~ ocirce o li tQ~ i

1t~Mgt 1 ~

- --------- -~--__-------------- shy

reg r ~~ch~ 2 ~ n~~

yt i Y~ e

5 lt )(~N~t~~middotmiddot~~middot ~ llW (~IV3 ) = - 06 t+=gtoacute Q-+ ~

~n ~ t ~ltPBA 1 ~

~~ ~ -OeacuteJJlt

l -i ~~

o) ~l L1

b) l~ 1

t) tl i

~BmiddotO

~i ~Dgt 6c-

~ li-t ) ( i - i) ~ ( r) t + ( ~ - -tJ I)n ~ (i - L )

ttTi

~W ~ ~1Yf l - L ) = 1 ~ 1lt nlto( --o n+

~

middotr

2 3 ~ 12 ~ L 3 1

I 5) 1-) ~1) J

2) t~-l)~ ~jl -i i)-i~ middot t-~)t middot3

Jl

1I~middot ~h ~ --ltI

~ 3 4J - - --I ~+-t - 3 5 l l ~ ehn --I I 11~

deg1 52-+L ~ Iz

reg

SEQJE-NCAS

~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

- Q ~~IY lo l1eacute lO ~Jshy~~~~=~ ~~t=~ -ltot YI ~) U IYV euro

~ L~t ~ J bullbullbull I

0)

-i~ Ilt ~ d

~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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Page 6: Apostila de calculo  III 1990 II

Wl~ f ~) -4~ lJlt Ilt -

ccgt n ~ ~ (

10

U4)odo ~II (n+i) V 1

Vl~ n(

li

-

~lt ~ ~iJ~ ~ MPc~ C-UM~ ~~) l~1clt MIacutegtie

I()~)~ ~ ) ~ lo) IJQM 10

) f(~) ((Ol ~ ) f lo) Cco o r 1shy

~ )

tt) - 1)Qv)( -+-lo) - IRN o o

fl)

~) _CoDt( tlto) ~ - cooo =- -1 ~ ) i

cshy-+ (t) ~ -(-DeuJ( J +lQ) ~o O

rt LV +4 (-1) 1(

~+~)

~h-igt Qn = --1--shy

(~n-~) ~ l H-il

L+i ~ l- i) ~

(Llni-t)-d ~

n-j)-1 ~~ thf

n ltgtOacute ~Y-) QM - I trM ~~uacute ltt- -1-) tl-cgtooS

i ~+~ lih-i) ~

~-i) lth4L)~ ( Lt -+- t) ~

Q~ ~IW ( 4~~ RV ) c 1 cgt6 h-tgt06

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i 2 4 I bullbullbullbull YL) bull ~31

-o

(lt ~ QVt- ~Vl euro J

i~ e 2 3gt 4 J bull bullbull J

at~ Q~l

l413~~H)O )

shy5ERlES

Ml~ CJo ~~do tk J)QJv~do o ~1fr1 Vi

~O

o) ~ b A ~ b ~1 ~~ ~oo)e bW- ~Q~ euro ~ Golf() ~ 11middot b

00

~amp ~oA - i1I~v1 ~ ~oo-~ ~~ ( c) COlt ~tft Agrave mOO WfAtildeDIi I ~ JJQJl p~~ ocirce o li tQ~ i

1t~Mgt 1 ~

- --------- -~--__-------------- shy

reg r ~~ch~ 2 ~ n~~

yt i Y~ e

5 lt )(~N~t~~middotmiddot~~middot ~ llW (~IV3 ) = - 06 t+=gtoacute Q-+ ~

~n ~ t ~ltPBA 1 ~

~~ ~ -OeacuteJJlt

l -i ~~

o) ~l L1

b) l~ 1

t) tl i

~BmiddotO

~i ~Dgt 6c-

~ li-t ) ( i - i) ~ ( r) t + ( ~ - -tJ I)n ~ (i - L )

ttTi

~W ~ ~1Yf l - L ) = 1 ~ 1lt nlto( --o n+

~

middotr

2 3 ~ 12 ~ L 3 1

I 5) 1-) ~1) J

2) t~-l)~ ~jl -i i)-i~ middot t-~)t middot3

Jl

1I~middot ~h ~ --ltI

~ 3 4J - - --I ~+-t - 3 5 l l ~ ehn --I I 11~

deg1 52-+L ~ Iz

reg

SEQJE-NCAS

~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

- Q ~~IY lo l1eacute lO ~Jshy~~~~=~ ~~t=~ -ltot YI ~) U IYV euro

~ L~t ~ J bullbullbull I

0)

-i~ Ilt ~ d

~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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Page 7: Apostila de calculo  III 1990 II

li

-

~lt ~ ~iJ~ ~ MPc~ C-UM~ ~~) l~1clt MIacutegtie

I()~)~ ~ ) ~ lo) IJQM 10

) f(~) ((Ol ~ ) f lo) Cco o r 1shy

~ )

tt) - 1)Qv)( -+-lo) - IRN o o

fl)

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cshy-+ (t) ~ -(-DeuJ( J +lQ) ~o O

rt LV +4 (-1) 1(

~+~)

~h-igt Qn = --1--shy

(~n-~) ~ l H-il

L+i ~ l- i) ~

(Llni-t)-d ~

n-j)-1 ~~ thf

n ltgtOacute ~Y-) QM - I trM ~~uacute ltt- -1-) tl-cgtooS

i ~+~ lih-i) ~

~-i) lth4L)~ ( Lt -+- t) ~

Q~ ~IW ( 4~~ RV ) c 1 cgt6 h-tgt06

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i 2 4 I bullbullbullbull YL) bull ~31

-o

(lt ~ QVt- ~Vl euro J

i~ e 2 3gt 4 J bull bullbull J

at~ Q~l

l413~~H)O )

shy5ERlES

Ml~ CJo ~~do tk J)QJv~do o ~1fr1 Vi

~O

o) ~ b A ~ b ~1 ~~ ~oo)e bW- ~Q~ euro ~ Golf() ~ 11middot b

00

~amp ~oA - i1I~v1 ~ ~oo-~ ~~ ( c) COlt ~tft Agrave mOO WfAtildeDIi I ~ JJQJl p~~ ocirce o li tQ~ i

1t~Mgt 1 ~

- --------- -~--__-------------- shy

reg r ~~ch~ 2 ~ n~~

yt i Y~ e

5 lt )(~N~t~~middotmiddot~~middot ~ llW (~IV3 ) = - 06 t+=gtoacute Q-+ ~

~n ~ t ~ltPBA 1 ~

~~ ~ -OeacuteJJlt

l -i ~~

o) ~l L1

b) l~ 1

t) tl i

~BmiddotO

~i ~Dgt 6c-

~ li-t ) ( i - i) ~ ( r) t + ( ~ - -tJ I)n ~ (i - L )

ttTi

~W ~ ~1Yf l - L ) = 1 ~ 1lt nlto( --o n+

~

middotr

2 3 ~ 12 ~ L 3 1

I 5) 1-) ~1) J

2) t~-l)~ ~jl -i i)-i~ middot t-~)t middot3

Jl

1I~middot ~h ~ --ltI

~ 3 4J - - --I ~+-t - 3 5 l l ~ ehn --I I 11~

deg1 52-+L ~ Iz

reg

SEQJE-NCAS

~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

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~ L~t ~ J bullbullbull I

0)

-i~ Ilt ~ d

~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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  • p111
  • p112
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  • p114
  • p115
  • p116
  • p117
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Page 8: Apostila de calculo  III 1990 II

~V7 OJ J~ ~lt

460~JD ~d J)Q ~ ~I ~~ YltJiO ~

U~ f1W d(Sta ~

VY~3W~

~~~~~~~tt~) ~~Th

i 2 4 I bullbullbullbull YL) bull ~31

-o

(lt ~ QVt- ~Vl euro J

i~ e 2 3gt 4 J bull bullbull J

at~ Q~l

l413~~H)O )

shy5ERlES

Ml~ CJo ~~do tk J)QJv~do o ~1fr1 Vi

~O

o) ~ b A ~ b ~1 ~~ ~oo)e bW- ~Q~ euro ~ Golf() ~ 11middot b

00

~amp ~oA - i1I~v1 ~ ~oo-~ ~~ ( c) COlt ~tft Agrave mOO WfAtildeDIi I ~ JJQJl p~~ ocirce o li tQ~ i

1t~Mgt 1 ~

- --------- -~--__-------------- shy

reg r ~~ch~ 2 ~ n~~

yt i Y~ e

5 lt )(~N~t~~middotmiddot~~middot ~ llW (~IV3 ) = - 06 t+=gtoacute Q-+ ~

~n ~ t ~ltPBA 1 ~

~~ ~ -OeacuteJJlt

l -i ~~

o) ~l L1

b) l~ 1

t) tl i

~BmiddotO

~i ~Dgt 6c-

~ li-t ) ( i - i) ~ ( r) t + ( ~ - -tJ I)n ~ (i - L )

ttTi

~W ~ ~1Yf l - L ) = 1 ~ 1lt nlto( --o n+

~

middotr

2 3 ~ 12 ~ L 3 1

I 5) 1-) ~1) J

2) t~-l)~ ~jl -i i)-i~ middot t-~)t middot3

Jl

1I~middot ~h ~ --ltI

~ 3 4J - - --I ~+-t - 3 5 l l ~ ehn --I I 11~

deg1 52-+L ~ Iz

reg

SEQJE-NCAS

~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

- Q ~~IY lo l1eacute lO ~Jshy~~~~=~ ~~t=~ -ltot YI ~) U IYV euro

~ L~t ~ J bullbullbull I

0)

-i~ Ilt ~ d

~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
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  • p124
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Page 9: Apostila de calculo  III 1990 II

VY~3W~

~~~~~~~tt~) ~~Th

i 2 4 I bullbullbullbull YL) bull ~31

-o

(lt ~ QVt- ~Vl euro J

i~ e 2 3gt 4 J bull bullbull J

at~ Q~l

l413~~H)O )

shy5ERlES

Ml~ CJo ~~do tk J)QJv~do o ~1fr1 Vi

~O

o) ~ b A ~ b ~1 ~~ ~oo)e bW- ~Q~ euro ~ Golf() ~ 11middot b

00

~amp ~oA - i1I~v1 ~ ~oo-~ ~~ ( c) COlt ~tft Agrave mOO WfAtildeDIi I ~ JJQJl p~~ ocirce o li tQ~ i

1t~Mgt 1 ~

- --------- -~--__-------------- shy

reg r ~~ch~ 2 ~ n~~

yt i Y~ e

5 lt )(~N~t~~middotmiddot~~middot ~ llW (~IV3 ) = - 06 t+=gtoacute Q-+ ~

~n ~ t ~ltPBA 1 ~

~~ ~ -OeacuteJJlt

l -i ~~

o) ~l L1

b) l~ 1

t) tl i

~BmiddotO

~i ~Dgt 6c-

~ li-t ) ( i - i) ~ ( r) t + ( ~ - -tJ I)n ~ (i - L )

ttTi

~W ~ ~1Yf l - L ) = 1 ~ 1lt nlto( --o n+

~

middotr

2 3 ~ 12 ~ L 3 1

I 5) 1-) ~1) J

2) t~-l)~ ~jl -i i)-i~ middot t-~)t middot3

Jl

1I~middot ~h ~ --ltI

~ 3 4J - - --I ~+-t - 3 5 l l ~ ehn --I I 11~

deg1 52-+L ~ Iz

reg

SEQJE-NCAS

~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

- Q ~~IY lo l1eacute lO ~Jshy~~~~=~ ~~t=~ -ltot YI ~) U IYV euro

~ L~t ~ J bullbullbull I

0)

-i~ Ilt ~ d

~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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Page 10: Apostila de calculo  III 1990 II

shy5ERlES

Ml~ CJo ~~do tk J)QJv~do o ~1fr1 Vi

~O

o) ~ b A ~ b ~1 ~~ ~oo)e bW- ~Q~ euro ~ Golf() ~ 11middot b

00

~amp ~oA - i1I~v1 ~ ~oo-~ ~~ ( c) COlt ~tft Agrave mOO WfAtildeDIi I ~ JJQJl p~~ ocirce o li tQ~ i

1t~Mgt 1 ~

- --------- -~--__-------------- shy

reg r ~~ch~ 2 ~ n~~

yt i Y~ e

5 lt )(~N~t~~middotmiddot~~middot ~ llW (~IV3 ) = - 06 t+=gtoacute Q-+ ~

~n ~ t ~ltPBA 1 ~

~~ ~ -OeacuteJJlt

l -i ~~

o) ~l L1

b) l~ 1

t) tl i

~BmiddotO

~i ~Dgt 6c-

~ li-t ) ( i - i) ~ ( r) t + ( ~ - -tJ I)n ~ (i - L )

ttTi

~W ~ ~1Yf l - L ) = 1 ~ 1lt nlto( --o n+

~

middotr

2 3 ~ 12 ~ L 3 1

I 5) 1-) ~1) J

2) t~-l)~ ~jl -i i)-i~ middot t-~)t middot3

Jl

1I~middot ~h ~ --ltI

~ 3 4J - - --I ~+-t - 3 5 l l ~ ehn --I I 11~

deg1 52-+L ~ Iz

reg

SEQJE-NCAS

~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

- Q ~~IY lo l1eacute lO ~Jshy~~~~=~ ~~t=~ -ltot YI ~) U IYV euro

~ L~t ~ J bullbullbull I

0)

-i~ Ilt ~ d

~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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Page 11: Apostila de calculo  III 1990 II

reg r ~~ch~ 2 ~ n~~

yt i Y~ e

5 lt )(~N~t~~middotmiddot~~middot ~ llW (~IV3 ) = - 06 t+=gtoacute Q-+ ~

~n ~ t ~ltPBA 1 ~

~~ ~ -OeacuteJJlt

l -i ~~

o) ~l L1

b) l~ 1

t) tl i

~BmiddotO

~i ~Dgt 6c-

~ li-t ) ( i - i) ~ ( r) t + ( ~ - -tJ I)n ~ (i - L )

ttTi

~W ~ ~1Yf l - L ) = 1 ~ 1lt nlto( --o n+

~

middotr

2 3 ~ 12 ~ L 3 1

I 5) 1-) ~1) J

2) t~-l)~ ~jl -i i)-i~ middot t-~)t middot3

Jl

1I~middot ~h ~ --ltI

~ 3 4J - - --I ~+-t - 3 5 l l ~ ehn --I I 11~

deg1 52-+L ~ Iz

reg

SEQJE-NCAS

~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

- Q ~~IY lo l1eacute lO ~Jshy~~~~=~ ~~t=~ -ltot YI ~) U IYV euro

~ L~t ~ J bullbullbull I

0)

-i~ Ilt ~ d

~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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Page 12: Apostila de calculo  III 1990 II

~BmiddotO

~i ~Dgt 6c-

~ li-t ) ( i - i) ~ ( r) t + ( ~ - -tJ I)n ~ (i - L )

ttTi

~W ~ ~1Yf l - L ) = 1 ~ 1lt nlto( --o n+

~

middotr

2 3 ~ 12 ~ L 3 1

I 5) 1-) ~1) J

2) t~-l)~ ~jl -i i)-i~ middot t-~)t middot3

Jl

1I~middot ~h ~ --ltI

~ 3 4J - - --I ~+-t - 3 5 l l ~ ehn --I I 11~

deg1 52-+L ~ Iz

reg

SEQJE-NCAS

~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

- Q ~~IY lo l1eacute lO ~Jshy~~~~=~ ~~t=~ -ltot YI ~) U IYV euro

~ L~t ~ J bullbullbull I

0)

-i~ Ilt ~ d

~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
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Page 13: Apostila de calculo  III 1990 II

middotr

2 3 ~ 12 ~ L 3 1

I 5) 1-) ~1) J

2) t~-l)~ ~jl -i i)-i~ middot t-~)t middot3

Jl

1I~middot ~h ~ --ltI

~ 3 4J - - --I ~+-t - 3 5 l l ~ ehn --I I 11~

deg1 52-+L ~ Iz

reg

SEQJE-NCAS

~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

- Q ~~IY lo l1eacute lO ~Jshy~~~~=~ ~~t=~ -ltot YI ~) U IYV euro

~ L~t ~ J bullbullbull I

0)

-i~ Ilt ~ d

~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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Page 14: Apostila de calculo  III 1990 II

reg

SEQJE-NCAS

~~shy lQ eacuteshy cL~ ~amp ~ut Utt ~ M )J ll euro ttJ

8It ~~ 3 ~

ltl~ lt f

Qt ~4 ~

- Q ~~IY lo l1eacute lO ~Jshy~~~~=~ ~~t=~ -ltot YI ~) U IYV euro

~ L~t ~ J bullbullbull I

0)

-i~ Ilt ~ d

~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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Page 15: Apostila de calculo  III 1990 II

0)

-i~ Ilt ~ d

~) s ) 1-) lt t-i 1l z agrave )

yiJ I zl Ql ~ 3 ---------shy

YtAgrave~ ~1A~m~ QIW 3 e ~~OYYYE)wt~ ~Qr a~

~Qocirc i~~q

Ltit ) ~ 1 -i ~ -1 - J

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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  • p114
  • p115
  • p116
  • p117
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Page 16: Apostila de calculo  III 1990 II

amp= tl1tj)

AI li licr- ~ ~llJ I I~ ff6~~C_ ~0~middot

= iTjlt-~ -AoOvv~ o ~1fl~ e bull

~ ~ D

amp

-ccedill = ~j = o t)j

b) QovJ)~ ~~~~

l~1L ~~ ~~~

l ~

Oil+J-~ ld~f-9iO -lt ~

~3 ~ J~ j~-9 ~ CLj =~ ta

- 3 --= ~lt-+ 1lt- 5 ~ ~lt+j ~

-o bagrave=- ~I

Z

1---shy

I

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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Page 17: Apostila de calculo  III 1990 II

-ccedilt--- c ~ 0 ~ ~j

lo-2ltr--o) l-z~) 0 -a ~ otildeb_2ti_j ~

lS=~

1 Zgtb- ~~- Jl)I)~ lo - o - ~j) =0

2

e~J) ~ ou ~e -SlC ~1

OlVde f~ ~o ~~ do~-~ ~I CcNl~ de CAJ~lt NctA~o

-1 1

7J-j-~~ -l~~ loacuteb-l-i)I

l ocircamp- ~_j) 32(atildeb -lecirc- f Iz o --r

-eCi O - t Iz - -

2 f2 lt 1

l3b- ~2_12)iz ~-1C-1) l3-~-J)

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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  • p106
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  • p114
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Page 18: Apostila de calculo  III 1990 II

C~J)]iJ) ]L

~) ~ ~ (~j) o~) ~ ~) J ~(J)

~laquo ccedilt ~ + ~ c1i d)t ~ lt1 ~ il

0)1

~ z ltP ele d-middot cotilde~ d~

J ~ ( ~l cf~ I bull I ~ )

(fi iel ( ~z f )

1(2 c ~ (1) t2 I I ~~)

ceY ~ Cf l t~ 2) ~ ~)

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

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Page 19: Apostila de calculo  III 1990 II

st~ ~~ Q(i~ u -WW1CLo lto~ampda ~reg

jlt ~L ~ (Qi~ ~f) CI~ n1L tp) ~( htz lampJ ~~ ~Cd~o co~~

sectll QJ ~ czf)J ~) ~ middot)o~ U8~ t~

~ sectt ~(fl -+ ~f ~ltrz -+ s ~_ ~~~ ampt )11 btl ~((l otilde ~ Dt

6~- ~ ~2ti + ccedilccedil ~((~ + -+ ~t~h ~ ~ 6~i U 2 ~(f2 6t2 ~f~ B2

6 _ ~t ~-t~ ~((I -4- -+~ ~ ~ - ~ ~ ~~i np 1)~~ ~p

V Y)

~ ~ ~( - ~ rt ~ i eurof ~tlt _ ~~-rsf~c ~~ ~i ~~ ~ ~ t2 ~ amp~ - nImiddot -=t)~ 6~s ~~J

(Cld A t 2 -tp

1shy

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
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  • p121
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  • p125
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  • p127
  • p128
Page 20: Apostila de calculo  III 1990 II

)~ ~shy

l~ t

di cl

(gt=i

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 21: Apostila de calculo  III 1990 II

L f~~~

IV~~

~ a~ - ~(~~I)= ej( ~~~

d~f g d~~- uf d+ iplusmnJ0 i t wj+ ~~f~d6-+ li -amp-l J1dotildeshyDi ~ ~~ ~~ ~tJ ~J8~

~ = 3i-j1 sectt 6t-j 1

~ ~

sectL ~ 41f ~~ 12~l2 bj ~1fl

~-~Q)~ j ~t 4~QOtilde bb- ~

d~~ b_j4 de+ ~jdJ+4~ Qb-~- t1lt1~j3dt(dy

~

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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Page 22: Apostila de calculo  III 1990 II

~QCf ~lltlj) 2rF_] ~-~ -t~OtildeO~ ~ ~ ~~1 ~ ~(k~ j lt2

~ ~lt4QiIl

O~ ~~ ~~+

~t

el~ltJ lh~ ~=1)

-1 ~ WII~i Sl

-1- tD-t ~~

(ebou(f~ i-O)

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
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Page 23: Apostila de calculo  III 1990 II

gtlt~ 3- f ( ~~~)- uf t~~

bull

_ jo -(~~ 1 L-) 1 Rl~)

S+~Cft06 -li _ ~~dMCffO() ~

d1

~c ~ ~-t ~ cl~ J amp dl ~j dl

~ lj~ JQoocirc~f 6~J-t-)~) IH ~ ~i iacutelWA Uuml t ~ ltt-)l- $MIl 1 ~h 5001gtUuml- toouuml-) ltoh) -0~) ~

~ ~ OJC ~wJ j ogtL ~

o-~~+)

o

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
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Page 24: Apostila de calculo  III 1990 II

-----------------------

3

[

~ cr (~ckt ~ d~ ) I ~ lt)UOP~l~ t~ d ( d-~) ~ sectlll sect dJ I oU

~t 61

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 25: Apostila de calculo  III 1990 II

1K1k~~

d~ ~~~ T ~ ~)f + + ~ J~ ~ - amp ~ ~

lD o -f (~lt14 + 5fJICt -t -T ~~ X+ (l - UJ 6~ 61(

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 26: Apostila de calculo  III 1990 II

e Yt

d~ bull ( ~ ~1ti ~ J~ ~d~ ) ~ ~4 ~

1) ~ ampC ~ I) = e-)IHiI ~-~ ~

~ ~~ e~6~i~S q l JJ( IJQM a i

~J~llGt 2X

~

- t)~l 4e ~ R~t 4 Q~ocircJW Q1 -~ 1e ~o Q~- t)l

~t (1 qn~

lf 4-1JIlM 1J d~ 8-~ocircfJj J(d j _ 4Z- l)eM 2j clj~-t-

Gilagravepe d l ~ _~I ~ J ~ L d2t~ le 1)QN~j dtt ~~ coltlL1 ~e- ~~j J~ -I- 4e OOllj (UL 1 +shy

~~~~ Qj a~ dlt- ~~vtRNl li diQ

~lf -I e~~ti ltk + 8 e~ ll] kdj _ 4 e-ljQAo Qj df

-fu1~Dil- Q)~ 7f (000 iJt) eL1

~w d3f

~ M~tz ltilR

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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  • p116
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Page 27: Apostila de calculo  III 1990 II

- ~~~Otilden

b l~ 2r eti

~~ 3

~~ ~~3+~ djU- 3rtdfdlaquosectl~3~~ b~~ ~ ccedilj

Or(1~l~ 3d2 (sect dgtI + sectt middotlt)

(lt ~j

q z K)()~) t1Co

~

~~ ~ _ ~ (f)(J14-) iJ -bi ~ __ 8(~J-)~V ~L~

rP -secte ~ _s (oftQI-) t1 oS I- fite -~ laquo~ -lo b I ( t lt1j ~ lt _~)lt-8-lt

( ~ 4-1 lttJ __ 4lcoD~)tL

~t~ 1~~ bull 8 ( eoolllJ to

UacutejJ tit

EJ gt ~ ( lJV ~) II-~1

Si ~2~ bull 4 ( flIi~)1 ltSf ~f 5 ( oon~) f~ i 3

j~2 _el Co6 gts) t1 d43_ lt4 (IIIIMJ) ~1d) dt l- ~ ltoO ~ )~djltk+ ~2t)t~ ~3

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

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  • p104
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  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
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  • p119
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  • p128
Page 28: Apostila de calculo  III 1990 II

-- ) t - ~ -~li V~- kkuYO l1YV vvJJlaquo1Jj 4e ltl~iWlMa~ dot ~ (11 ~lt ~3) bull ) ~I) ~t~~ ~ r~-l Ccedil -e fgtt Qlt ~-1OtildeOQ

dj = df~ ~tl~i~ 1Sf~~~~Alt3~middotmiddotmiddot-t~ f~ b(i S~ t)~3 S~

~ Agraveli -t ~ AcirciZ+ -+ ~~ 6~ -= J ~i ~1 ~~ ~~

~ e O J ~ e O J ~V~d ~~

LAJt oM2+ _ -+ O A4 I OU ~Q AgraveOCU d~j g~a ~ ( L 1 )-1 (

cl f _ sectI Aacutef (f 11 f ccedil~t A~~ f Agrave ~~J t=-gt- ~ O-Agrave~l dtt

Agrave~y dlth fl~middot ~ 1~ OfJ + OJj dr

ki amp~i) A~L- d~lt I AIiVc J~

tl1 I- di

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 29: Apostila de calculo  III 1990 II

hjT ~ k i ~ ~i

-amp~

dj Jf ~ ~d~ ~~itm j~1 ltt~

dj ~ d~l+ ~ ~(l-t +~f d2t~ I e ~~ ~21t ~ ~

f 0- ~i p ( lJ3) Acirc~ lt-I-Ad l j+ Ai) - ~J lll 1)) j tt Agravex A1 hL od h7r O1-~ ~~Jchj= Ql

datilde- )Agravelt- ~ocirc A~v dj

d1l ) diacute ctdj gt ( o ) ~ 4 oa o)J

l~L~+~) lh~ o-~ A~ -e ~ (~-tA - euro -~))

llt lt11- ~j cllt ~ ~) d~

amp JQIIi ~ 1- ~ - co1 1 ~

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 30: Apostila de calculo  III 1990 II

1shy

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 31: Apostila de calculo  III 1990 II

Ci~Jo

~ G)

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 32: Apostila de calculo  III 1990 II

t-~-- ~- - -shy

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 33: Apostila de calculo  III 1990 II

a fi-

- o~ltLuacuteMlJlJ L rlu (~) -1_ ~ - o) )( lo l _ j Ilt

lI_ta -jo ir- ~~ ~ CQ))o~o ~ (Q Oacutea ~ WtyJ)

ct)ro (~)~O~ f~1 ~et tu(l~

~ ~- hJ

CWO -10

LI -1)(- to) + l1- 02) la) + tamp-3) (~) o o

Oltt -+ tIO 4- 3 - b 8 -2lt = o

~~~~ ~AL ~ltVlt~~lY~ eqU)~ do blttViacute~) Lc o guoe~~~ ~ 4f ltlaquo ---t ct

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 34: Apostila de calculo  III 1990 II

__ --_ _ --shy

l~_middot_middot_middotmiddotmiddot-

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 35: Apostila de calculo  III 1990 II

-

~ - ltsect Agrave-= + ~ A + ~ h-r + ~kf e1Agravej + E3Lj-) totildeo~ Agraves tt ~Q 6 ~ ~ -x bs 6 ~

t ~ = ~ QQA 06 + ~~ ~ (lJ m CQo ~ t- tt Cot Ea~ g Coaltmiddot ~~ ~ ~ ~ a

~ ~ ~lf f ~ rtJJj~+~ ~~+ ~CDAotilde-4- ~CooOiJf- s~+~Ccnil450 ~i Agraves-+o L~ ~ C3- j

I

ltbu ~ Qoo ~ ~~ ~ecirc -+ ~ coo ~ ~ ~ i5j ~

l-

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 36: Apostila de calculo  III 1990 II

-1

I

l ~ 3 s

- -~ ~ l Ll~ (11 t (~i3)

Q) ~ ~ ~ 3t b) ~~ ~t- -t s(

- - _J ltJ -f ~

~ ~-1gt3lt- j -K ltt 6Ji - ~ li

~~~ (~) i ~j 65j r ~ f lltbs)r

~06=_ f l~

~fo _fl__

~

ltJgtO~r -3

Viacute4

toe -L + oacute~ t -+ toa ~ ff4 Vi4 fi4

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 37: Apostila de calculo  III 1990 II

~u --- -

G~ocirc

Jk =-~

r

- ~ -- - --- ~-~--~~~--~ ~------~_

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 38: Apostila de calculo  III 1990 II

oishy

) li I~ j 4t tVJ

r (J

2ltocirc~ u~ 3C jltshy -- ~VE)cJ 3 U)J _ Lu

~ ~ 6J - lJ

)~J

secti sectt Dltr+ 9- ~ = 3ihJ ~ ~UltT) ~ lk) ~ btl-)gt)U~T fl UU ~ ltt)U amp1 ~u J

()~ ~ Ccedil~+ sectt ~1 = 3~middot njo 1) ~~)~ oi(h~lJ+~u )1 ~ ~~ ~j Ccedilol 1

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 39: Apostila de calculo  III 1990 II

~) ltampdobull 2

06 1Jr fjJ2Jt Q lf

(~ ~(jv) ~

~

~~~~

-uv U ~~ Qv

~~ ~o(--- ) -

lt5u ~J

~

~

( 1J ~l = 2gtj I)W l aJ2-~j

(J

ccedilt ~e j 3 (OO lb-shylt

Ji MJl u~J~= ~1

~ IJIt _Ia Qshy-_

~lAgrave

ltampD~v91= ~~

uv 15GJ JJeuro ~ - 2M iQv ~J CcedilI ~I

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 40: Apostila de calculo  III 1990 II

---

J ~ u+ -1+ ~ l j ~~ ltJ3)

~ ~ sect~ ~ -t ~~ ~ lt6 u 1)C( lt6JAacute G) ~~

~ ~~_ ~ce -t 5~ ~j ~I ~ltt ~I ~j~

~~ ~~ ccedil~ 4 e )i

bb- ~~ ~~ G 61shy

~j~ e ~j

E~

~j~~ ~l - e ~J

e ~ ~j~ t Qj i-+- e ~~ ~ltmiddotl) Qu

bv

~ ~ ~~ lj lI - lZ$lt u~ eco l~ Iacute) 3 ~ ~J

lt 8-~ 5) 3 ~ t ~ ~i lj 3l1- ~ 7t-~ d Oooacutel tmiddot i 2J

6b

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

o ~~ I fllt O)~i)

- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

o Iz

1

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 41: Apostila de calculo  III 1990 II

~ = ~ ll)QNmiddotdJ) lc a~) E-oltshy

ccedil~ ~~~ lQp~ Li ) l ))~( ~~) ~j

4sn

d~~~ agrave~~ ~~ ~~ ~ dl G~ dl 6i 0 E~ dl

dt ~R--~= a (1)jII ~)) (Jeurox aJ ~i -t tli l to()fll)l~c~~ e soltl~iT

+ ~ l)YJ -j) l ~1l3-) l JeC 1ampJ et~ ~l

~-_ bull_--~----

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

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) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

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L~Iy ~ ~-ce- 1~

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- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

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) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

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gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

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-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 42: Apostila de calculo  III 1990 II

i I 1(1-1--middotmiddot I -~- j

~

CCJ OI -)i) t~iacute~iacute~-Ej~~J ( PI~A f cr~CccedilR~~~c~U- CcedilJ()l

eacute XTC~_ IVl ~~t

- CbN)Je~ Cl ~UM~ C1rl~~ ~Y) s4~ 9UJL =gt0 (oi I Q2 I bull Q~ ) ~)CAtilde for40 tX1REMJN1E ~ (li ~ ~n )I

~~ de~1 ~ -J R~ ( Ui QtQ3 ~-lI))= o t~ ( Q I uuml~ 031 o~) o l~~~

JNdo ~~~QN~

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

ltt)~ 8(3 - bj ~ 6(f ~ ~ Qj- 3~ ~J

J 7

d5alto

~e - 3 ciJ 2

~i

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~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

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r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

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- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

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) ~3+ ~~_ 2l$ o

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b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

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gtltt--10

~3- i

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--

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-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 43: Apostila de calculo  III 1990 II

s reg

4

~~~ ~ O-~ ~(ojJ) IgtOtildeD eacute ~~ (tMJ ou MM ~~J ~o ~laquoC~~ j _~) (j_ ~Z)

3-= f ~ j) )~ 3j2C 1-~1

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J 7

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_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

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) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

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1

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) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

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o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 44: Apostila de calculo  III 1990 II

~e - 3 ciJ 2

~i

f5~t ampt eLj2

~~ fS1 ~f ~~

_- - b~e l~ Ccediliamp

_6 2e ~e~j Ccediljllshy

i

CC~tFjs ~jJn(Ltjr[ MCcedilltA =J~I(Atildeiacute) x liJ2 fA-AacuteI

~u 3-= 4(( ) ) ~~agraveo ~ di~ bcLYVOHIIlolNlis 10 L~ 0 h~ R ~ ~ -$cllj) ~~ cl0V~~ k~~ o ~ OttoQfffi 1 ltn~CIJL (11V~tVUA Qlaquo j (PO ) C ~ ) Q cu~ - ~ R~ ( gteoj) ~ O l

Q~ I) 1 (~I j o ) ~ ) ~tjb ~~ JjM6A~f(~ ~lt~ l(f~)1o) ~~i l~ jo) )

- ( eco 10 ) f~ ~ lto I ) o) f~ (Cc)l)

(~ jo) gt o e ~lltll lliacuteo I )0 ) lt o ~ gt()l~lraquo eacute Mil~ ~ l~ jo) gt o e f ~ l~ jQ )0 ~ lltfo~) -ecirc ~~O

l4lamphj~)lt o ~ ot](1)) nnoe r JI~~laquoOAeacute bllltk~ Jle decde dCt ~~~ ~~ l~ltjo) = o lt2N~ ~

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

~ t ~ - a - 2) o

-- ~

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L~Iy ~ ~-ce- 1~

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- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

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1

o

o ~

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) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 45: Apostila de calculo  III 1990 II

~a~a

~ 3-c- 5-0

t5~

G~ = 3f- 1-0 ~j

r 3tf2_ 3~o

) 3j~- 2=0 31~- ta-o =l- J ~ ~ 1- ) j - it

l la

0) (-i -2 )

h) ~ l (-i) ~ )

e) 3 ( I -2 )

d) f4 t 1) a ) _ ~l-lo~

1mk~~ s~~ uQX~

-i)+3 (_z)3_ 3 (-1)- 1lt l-zL 20

- i _ f) t- 3 te -t eo

38

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

111 -- tl o

) ~3+ ~~_ 2l$ o

L 1i-i~o ~

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) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 46: Apostila de calculo  III 1990 II

b)

lt o v)~ i ~oV-o d-e selc ti l-i a) e roV~ de ~

C) ( 1-2) t lampI-~ )=- ~ -~z 1 - - -la lt o Lo~o i ~lt)Vo d~ Se-o

~ l~I-2)eacute ~k

~ l1 2) = 6 o __ tz o I lo lI I

b 0 deg 1~(1z)70 e0

2r-~W a

) la ~ t4 ~lt - t-- ltI = o

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) ~3+ ~~_ 2l$ o

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- J4 o- (O-t) 7shy A lt o ~~ c)O 4

o

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1

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) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 47: Apostila de calculo  III 1990 II

-- ~

Co~ccedilatildeJ 3~Qi~

L~Iy ~ ~-ce- 1~

~I~~ ~f

3ltt~+ 481f- e1 l~l~)

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- J4 o- (O-t) 7shy A lt o ~~ c)O 4

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1

o

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(1)1) gt0lt ~ iO u-mk rba f3

) 6~Y ~~K)

) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

t - f + jt ot ~j)- ~ o

~~~ 1

_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 48: Apostila de calculo  III 1990 II

o

o ~

~~A 70

(1)1) gt0lt ~ iO u-mk rba f3

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) ~Ilt ~+lt1amp ~LUgtM~ 000 fO~~ ~~~ e ~~) de ~ l_ I b~~l1)j) ~ ~+J -~f1

b~q()n ft~Q1UQ tt o =- ~ -= g~ - egt 0

~~ Ccedil~

~~ o p te Ocircj~ - SCi 1)

ltj ~1

3ft- ecircgtj o ) rit - j o

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_~~jJo

o-ct+tl -~ - ~4 o

gtltt--10

~3- i

~

~- --- -~~---~~~--- ---~-- -~- ~ shy

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128
Page 49: Apostila de calculo  III 1990 II

--

~i l(Jo ) o - 3 - Agrave lt Ote l0) =

-~ O 1 ~4 til) It( 1) 6 -3 ) - ~ 70

-3 amp

amp - Ca o~~

amp2

___-i

  • p103
  • p104
  • p105
  • p106
  • p107
  • p108
  • p109
  • p110
  • p111
  • p112
  • p113
  • p114
  • p115
  • p116
  • p117
  • p118
  • p119
  • p120
  • p121
  • p122
  • p123
  • p124
  • p125
  • p126
  • p127
  • p128