Math 1203 Test 3

Ap「ii 27, 2018

Nam。: Sc,Lu丁I C測S

Note that both sides of each page may have printed material.

instructions:

1. Read the instructions.

2. Panic!!! Kidding,don’tpanic! l 「epeat, do NOTpanic!

3. Complete a= problems in the actuai test. Bonus probIems are′ Ofcourse′ OPtionai・ And theyw川

oniy be counted if訓othe「 p「oblems a「e a廿empted.

4・ Show ALLyourwo「kto receivefu= credit. You wiIi get O creditfor simpiywriting down the

5. Write neatiysothat i am abIe tofo看low you「sequence ofsteps and box youranswe「s.

6. Read through the exam and compIetethe problemsthata「eeasv (for you)first!

7. Scientific caiculators a「e a=owed, but you are NOTailowedto use notes, OrOtheraids-

including, but not Iimited to, divine inte「vention/inspiration, the internet, telepathy, knowIedge

osmosis, the smart kid that may be sitting beside you o「 thatfriend you might be thinking of

texting. ln fact, Cell phones should be out of sight!

8. Usethe correct notation and writewhatyou meanは2 and x2 a「e notthe samething, fo「

exampie, and l wi= g「ade accordingiy.

9. Do not commit any ofthe biasphemies mentioned in the syIlabus・

1O. Otherthanthat, havefun and good Iuck!

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1. (5 points each parf)The haif-Iife ofcesium-137 is 30 years. Suppose we startwith a lOO-mg SamPie,

and iet P(t) 「epresentthe amount ofcesium 「emaining aftertime C.

(a) Find the d辞e「entiaI equation satisfied by P(亡)・ AIso inciude the initiai condition・

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(d) AfterhowIongw川only lmgremain? 一塊も

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2. (20 points)ThevoIume V ofa cancertumor isgiven byV = 77X3/6wherex isthe「adiusofthe

tumor・ Using math he lea「nedfrom 」hevon′ a doctor estimatesthatthe 「adius isg「OWing at a 「ate of

O.4 mm pe「dayat a pointwhenthe radius is lO mm. How fast isthe volume ofthe tumor changing

atthistime?

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3. (20 points) Afarmer has 2400 ft offencingtofence around a rectanguiarfieid that is alongside a

Straight rive「. The riverw紺form the borderofone ofthe sides, and so he needs nofencing along

the river. Use caicuiusto assistyou in findingthe dimensions ofthefieid he can fence around that

has maximum a「ea.

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4. (20points) Ske・tChthegraphofthefunctionf(x) =震-3x2 +4= (x+ 1)(x-2)2byfi「st

finding (provided they exist〉 the domain, intercepts, aSymPtOteS, local ext「ema, inflection point(s〉,

intervais of increasing and decreasing, and intervals of concavity. The preceding must be indicated

On yOur graPh.

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5. (2Opoints) Letf(X) =X3-3x2 +4,findtheabsolutemaximumandminimumoff(X) onthe

inte「vaI [1,4].

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Bonus Problems: (You must compiete aiI p「oblems inthe actuaI testto be eIigibie).

1. (8points) Using Riemannsumswith4subintervals, aPP「OXimatethearea unde「f(x) = 16鵜X2

onthe intervaI [0,4] using ieft hand endpoints. Show a= you「wo「k.

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2. (8points) Findtheexacta「ea underf(x) = 16- X2 0n [0,4]. isyou「approximation in p「obiem

l an ove「 or unde「estimate了

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3. (1 point each, aii o「 nothing!) Completethefo=owingfo「mulas.

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My pian fo「 passing this ciass?