AIN SHAMS UNIVERSITV

FACULTY OF ENGINEERING

Electronics and communication Engineering Department

Course: Numerical Analysis (pHM 665)

Assignment #5: Roots of Non-Linear Equations

"Problems in pages 37, 38, 39, 40 & dl,

a'\"r#NJon t'neo't

LFcxl= i--3x =o y')= ??_ {o'oI ArGrt

l0*<-+t^ ,tD)trsD)

" Zirer

SttP'

Lyz n 7 aL-sl

fil)'''\'?\-zt

r€ QL, z) (e*Jt"+ g-*t...rt..* "

:lc=qtPEr+'a:?=i

e'= 5*ro(Flt) =s*t[o-S

-'a9j!---*k#:-Sf

Y=*=:#

: tJe ;5ft1o

n/L,A,; -

Lae-h!"

,

L &r Cr a ib i

\ Fc^,') f.in \

l- [.Ur'/ ficu;c:j t Trx-Y9, -o.3 [,;:71/

.:- - ./J-/

A'->',/: '.li 7'

L 1{s "*f,2 ./ ,/- -/^'-/ 1t-20;<o I,/ ,....

ayi r- 3

z .tk5n o.5

f -rf# o'Lh

e s /,,.,.juJ dlre,v

r)= \

('rrt*ol,* r= r- E \zt )

' f*r,-rl < tF+

,\

1,5J, 3 - t'5tzt I = D'ot1z.i I

t

b- q r7T : F :o-oj)Z

Z

(tu l*n-t )q LSsAu'l OLtwr

zn*, = xn _?cxn1 ffi z,fe Lt,z-a:%qh__

n['*@- ':

6)

L.--.':. ':..:..:;4ab

ttti+il' , ,ri:., -

(i-:(:)

uI

fla-t I fl* f!*"'9 Ftr"lJJ.a t{3) 'o'2811

'*,* [:sto\&a** @B rtrfu Wfltffi : .,'."'..('

,l,r'LE{r@

et.1??L

,.\

L!347 btazrHL*lo:Y

l,nt{ r-:;\,i

b

t'nrv 1 t."Vv ,)4 -.-,,

-o.fo55 :o'" sl {a--

l-5 15 z

7' 'sJz-

-r'I,E,l *1 l.Stt 3

*-o.o31L 4.gttr;

E^q2 nfr

= j.3 +!*

)L

Yt*1' ex -3 "c\xo

f CN> a e'-- 3

/tr'( ,l = 7'39 1 "re,z* -_ 3.*.5'2 = \,\

;, I i;-;.1 ; f )5 tt 2t

^.L\,t 1

I - n1 I]nl\- lg Ft(re-,) I

.2

4t/,<LYI lv^t fl'cxnt Fn*1

O t-5 -o- olt.ti l,4gt7 l.s lz3

L2

t .t tzs 9-Sq:+ rit t.s31L l-Stzr

/-s, z I 2Y:;l &i, l'5. \ eJ-r.rfiEcrts+,FR@t&

lr[J3T.)l

9''t u' :lo bs :Yf$'-: S.d Qu) {-E lr

€ =3x!" er ' 'l^3r /L-_f Cgbx- Lr fi

X- : J-,a 3Zt

a\r t) =. a t6'tntl< t .zn. q-f..E. = i

n

U-

/n

n

l-56t-{ I

' l-So 'b Y

/-5a63- .,ti

t -C^Q.L/- 50'lb

**=--s;1t . la49l, /-5lo/

t6

)1lo Ll.s nt

*D

,-S, I I l.S tt q:=-

% = ,-s llLl

Ztk,4- l*r-'I =)t'\ttQ-

I:tx) = Lz,3 + 42r- - z2z -I

GrrcJt 2D

1J

--it

-11/t

(r€t'-s' -

"5ttti:

-q)56S-z\Lt-15

= -3'utJ{

",t>Y\e-(1, t-zS

{( "'zs)! t "-S )

! 1 *':.rf-(t)f (r,zJ)

$

<5

7.

*

:

-)

.Ia

a'l

=

i.l

z)

/?

d,

'-

a

(

(

(

tL

(

{.

(

{

"frIr{

l-

IPr

)=

)'

g)a

*)

-t)a1- L/

-3)-4)

= _ s)-\S(

? o'?1) = o.c>1\/ ''

-l-t

'25 )t-s)\, 15

z)

* t-'f c -

t ( -

(e ( j F'-21- , rz5)

,),|,;.fa

b,s"ci,;. !tS\.,

6'=.5+3'- n) "t"(t* ),: *nJ}S),. n74. ;Ei A; c,' \ f,i FCa,') ro, '6't , -4-b 5

Il)'t' 't'' ;

tfr. .,/'t.p{5" -t i4,

2 ' ,y''n t ,, "i ^rt.r:{ ) l- l7 c, ')/'^ -r{ ltn

'..--')u ' ..*.u /-j/, '.:'t-,/ cr6

\ ',p0) .{;-ryg /-o/4 S ' :*l?/" -/'-oYu

Tr*;:*-^-.

=,'o3Y

a.Z.Z*l=-%,,

--'o -D-{Wt.6 64 i@Ll

L )'olt7 )44 -o.ogT

L I,g? l'a? ? J K6t.olt) : /-o195

A fi seco;t l-l li.,l

r€ (r, \-? 1

/n-t f@n-t) 7n tt

-t /. ogVLt

l."l l o

FG."i

.L5 L3

t.o 6/4-r:.-,.,.....,-.-----."..:.-.-

l-ct74

I,

W#'-*'

I

r. -6f{3

l.o13Z-.e:ss^-

*+,\%r*_

r : -, ..-r !:-r;

^o.ot Sg 1,t'5* tia i ,"JB'--=---**

r€ ( ), t-zs)

22/:+42t'- zX- S =s

X='gtw)

dc*l?-3y +\z<.

Qr+ "&

- ?o*'l'? S + 6.52< _ o.! ,f g

,.-----.-___,- _(l-usta!v-o.\*\( t,2 5 < o- f 2< -o.\)(' )'-

z3* z*- a-5' z:*d! 2's

4frL= 5+?i&;24\.,2-Z,- =-l,Zf + o.\,x,; o:,\;

Z : LL) _+ .o-tj ,i- - v"' -o-J-z

7z') = t+ -o-5.v-*o'!\--zx'-L

*=

/=

!-

Vtco) =

lfr 14 l=

_.).z t _ 7z-;z?

<j-\v - o-s

fno')V-

o.Z7V

(-: -l-J o-)

? t,)z7-) z

rr\,-\ x ,)

)

:)

.l

l.',

/t

7

t-

tx.\(*

(t\()

ac'0

a'

la\

i ,:, ;ij!.

I

L

l.a14l,'

/*fql 1.-o 671

"/)5n,.,',,..Je,,,*^'-F*t

a

/r,t-&5

1 -*{ 541

q I -a t3J

4' I .o-15 I j . -......

I

trt*.t = &25 + ,'f*- o*5 *)"'

2(a* t

f-oq.?t

tr.aV J S

:'-' , :,

%,- =,> l;a, ,71i"

i!

F(r) =

F7*) a: ri!

zz3+4vz-?/-Etx'* {F e

) re C) ,l-z \)

F?4 F /z,-+ d f- ( r'z s)

n''%

o2Cn f @n) F (rtnl).12s o.$(,oz

8l l.o7)SI

, -o.rr1Ol"Fas&e,-.-- L31'11 i

2 l-o115 o;ttzt i tt q$? t-*17)-o 771

(

@neu,,l-n i )-1r1tn.)

fr*; i

f'u) Z3r #3 C.) ) - \1-

o

='l-1-z-rrr3=-a-2.t\

i-E n +3 * c) re U,z)

l) \ n \ . 9tY (F) c"

7+*rq-r L3

/.q

l,g3y

t;= zx_ I +t

)"tu : 7--* K,l

Xo*t

DLcv.) - ^, afb-F;; ) *6-- -,

P i"4 l)^,

1.5

,21t3 2.t27 8.lq q

5-s 3

(tr) 1/r"/,;" )4r,11",.1'

lrrO = 2z'3- 9r +..e-- o

5H : x3+ 3

7 a t *'*?S3 t*) .* t *'* 3/5

t'( r) , z/5 v'g't*) :, l-'4 > t x

t, s,_-'3 ''7t 2 y? ?yu

itr), W-'&" -*---_,___

E- sx j_ -1 frV*s= /,/'

-r.---

"rr'- 5 )'

-?L= _- -

' C*"- 5)

A t-nl = ,,.-r \ .-\-/ ^

( *'= \)

U'(il =- z(y"-

ott,) .4(-- q) z

", -3-\ 9

g't4 =

3r*t 2- 1l( h-*)\ff(il: c( t)G-x)(;

7t-sx +1 -<)

r' (r' 57*\s = - 3,?

-. j

iit"= - .x- 9/yz

lr\a/ - ) .-----\)7-vr-*f-lz

- lJ

@a'

v.z -r)fi'til = rp-+71

ooo il e,*-*n *t * a f t\ ;;L4e* Al, yr&.** s ff

3 S--'i,oi t*"tq- N.,o- qu'$;^'-J^e^'-' S

. \) 1. -.,..-; )-s*/-s**"\i1q*c*i*d1. tt,'; <t*.:

,

"- fT'

n

/' * l)'--\V'r l- = 2/

-r'/-

;{- , L"f J/F(x,l), [t" J'J'=

lT^llH:Y"t)"r@].fi-)--\ On' t n3

-'Yz

b =V*-*.) \-/^

r tl L-

Gtx'y) = /x-x )

C.-g,t)

-v"t, (r*- rt) -(z

a'51? < t= o<1

L, l't"oi""d ?€ i *=h-

$ ,., = [2l".* * K*t ]

,%n I )" 7nt,- J n*-\

s-S

, ' ...-",

-t

; 4osl'

.MW.Lrw

4

''tr-

Z o o-9oL

1\

I

I

II

iIII

I

1

5DZ'+J"+*=o\

\J!

fr=t-{-*'",/L=u d'-?r]'

#t{4/#.t, , * ,r _.)r" (rA\,L?-d-? / :vo

u#-$-rub* (r-s

tt;/"-ffi]

/*C -t-.<,

z -- (r*J) ".\\

-lH ,ot\ -2\L76 i q- rba

t@*Y) " * Lrlx r3j vz-

_ [x-f)L.,- ta-3 <\

%nd

U

dn+t

?n*, * (o^ *t")h

I

? o-11 <11

#"1

.\l. clnr( ,

d,

,.Ls*"\,.,,.,..,

I'.t 2,.52J9.,O,t;L 1. { e32,-

z-szqtr-(qjz 2.41tq o.Zq rS( 'l' L(+:o-25

'E-tell\l@€sep#tl

2-uSz4 |

2.Lt1"yl

_*w:I::,-zhd( \'-t ilt+

J.LI Y Zq a.ZQ alrE

Fr%.4

D, zq3q-.r'<;, ,

)-!Jq+,-"thE,Eq+

t-(so.=!!\r._---.-___-_/

I ' {t:s

2'!:1",

o,2q3 4 t-ts 2-4!36 o .Z41, a.#.-

2.q1o^24l^[ s

(