2008 Calc Final s

2008 Calc Final s - PAM, 200% Pwm, (-3.ng 2 1. Find the...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: PAM, 200% Pwm, (-3.ng 2 1. Find the following limits (5 points each), giving reasons for your answers. You may use any method from this course. . VaH-Z—x/fi -——L Liv—*2- 1r —2:r a ' W1: '53; 5?». +57; Q: +2)-—1y. a yet Weft—1) I firt+fiy " «pm, vcv—flCrJWHrag ‘ m , Q . ‘M __ *l _ F .1, oval ¥M(mmo 7. (14—1.) 3 _\ V 1*» ‘ ’2 7-— l‘l’}; : g 2 = G w»- l ' Q: So vak a 1: Q “159°” . ,_ '25— C hm 5111(533l—539: _—-- .r—+0 3’; Q Scan-s -Z$‘3'3~§¥ _ ~42; «my ————-——-'—'__ :' --———‘—' _- (a '35—'50 3“: )c-aa (9% "ac-$9 :: “LL—S— 3 2. Find the derivatives of the following functions (7 points each). You do not need to simplify your answers. 1 a. If y = tan(3:c2 + c) then — = 65L 51.94, (gk2+e> 9%: = @hzflk‘mv‘ (GK) :2 1, b.Ify=efithen:—y= (KPH) 3: x.— I34 ~‘R fl? — (fife --§:C%. =93“ M , : £23" 4 3. Find the following indefinite integrals (7 points each). -1 ' __ 3 a- ft? —t3m= we we we" we 45"“ you = '% 4"” ' : r V'“ C, Swat’gJ“) 38 W k "r r gt 3;”. [I-t’N’C/ 4. Calculate the following definite integrals (7 points each). a. f3 In?) dx = HQBW Uni?) 5” b3 My 5 3'09“ l 3;- _ qwr—w‘) du-iw I, L flat 2’ '¥ 2 lla b. mks—1073:: I ’ ’3. 1.. by, 30': S@+.)ul‘&u. =SOQL/f“ >42“ dlu-rcflv ‘9 _ an 9;“ / yrbU'l ' G) i) o z t %+ %)=(%*7% n. :2 ‘@ 'Tg '5- .r:-. :J-I iJI'IiII‘LH lie-“mun” LJSII' :1.Pl_'i'. under [hr graph 43.1 ‘I':_.-_-_: :r: — ._'._3_' [J'biun _,-_ _- H 1_.'. r — .[ II:-ll'.|.'l :‘i 'JIIIIIIII'L' ill-Ill"! .LlJalltmlmMJlIJ-L I~"I'l.|ll.p.|:1- .thl hprhl rudimufig. '1]... "1.1.1. ||....-1..- I-I-H”; .uEwnr :n: r: mun Tuu wflJ mam-m: 1m :rulil I—nr I."'.T.1|I|.‘:.Iil'|.g Hm: jnch-mI {Wu-EU]: | a'I-p-J-Irmin'lmlh "will fr. 117: |nII1IIh |"'II|II 1.III:'L1|IIJIlIIHLHf1'111I|II1|||.;|.I Iml: LL'. ll';l."1.l.ll'".'l_'!lifl3l'_1'.hl_'d I:_'..' T-rllllr I :y'! 2.: HT 1hr: paint 9.2 H .-1|_||.‘.' rum-Ir. I‘fi1l.‘lr.!|'-Ii nape-:"ifln-ing Hui-L l'uu- u.- .urnlatrfillu " mua 4-5113‘H5n31-a' ‘- CI 3.5-1.4 4 {-EEB' + {is-133' '4 fl- '1»: 14‘;- ’5' an} n a '1u-rm fl" '5 1II'.I'. :I-‘rlmi itnll '. [:a-rIH'I'.rIIr-I2.ur In ::|-- '.||r.:llrl||l Elm- T 7. (14 points) A radioactive frog hops out of a pond full of nuclear waste in Oak Ridge, TN. If its level of radioactivity declines to 1/3 of the original value in 30 days, when Will its level of radioactivity reach 1/100 of its original value? Note that this is an exponential decay problem. RH?) : Ra Q: ht 42-30 'LR/OL‘R/O‘Qr MGF‘W“ 'QuBS h = It?) 30 8. (14 pts) Let f (3:) = x3 — 12:1: + 5 on the interval [—5, 3]. Find the absolute maximum and minimum of f on this interval. Absolute max: ‘1 y .- f’rm 3x’z'l7r = goo—v) Lillyvso k:i7’ 8 9. (14 points) The graph of y = 9(33) is given. a. For which values of a: is 9(56) discontinuous? Don’t worry about the endpoints at —6 and T in either part a or part b. b. For which values of a: is g(:c) not differentiable? 9 10. (14 pts) During the summer months, Terry makes and sells necklaces on the beach. Last summer, he sold the necklaces for $10 each and his sales averaged 20 per day. He also found that for each $1 increase in price sales drop by two per day. If the material for each necklace costs Terry $6, what should the selling price be to maximize his profit? Tmhfmq.?,30 mmeaw M mm my 395;,“ 200°: Mam. reverbue Cost M M P —: (lomM'Lo-IA fl, —- Cello-iv) F; Ly) (10-11:) [LtJrfll—zMUH'ZO'er-l = has—2», rag-Q»: 1: 1'2, "(x P'ly) = 10 11. (15 points) An open cylindrical can (without top) is to be constructed to hold 16w cubic cm of liquid. The cost of the material for the bottom is $2 per cm2, and the cost of the material for the curved surface is $1 per 0mg. Find the radius and the height of the least expensive can. (The area of the curved surface is the circumference of the circle times the height.) h 2 _. =L£-_ C: z-ar‘ntrh V"‘9"7‘“"‘° *7 1" rt It. _ 7' G 2mm zed—1%) ~zmz+wl7 *ZFD .. i I L: C -Q'ITEZ‘P— rm] “L [.9— rgax r' W QV: If,” 11 12. (15 points) Use linear approximation or differentials to find an approximate value for 3 8.5. aw is) a: 1%) mm (My —2 “8‘5 livmefi “MEWS-55°) W53 '1: z+£ll~1>55> = Z+£Lfi 5% 13. ( 15 points) The altitude of a triangle is increasing at a rate of one ft /min while the area is increasing at a rate of 2 ft2 / min. At What rate is the base of the triangle changing when the altitude is 10 ft and the area is 100 ftz? I , -2-/oo«l ([1; 20+ '2- 2 Z__/°_o_ cQB _ no __((o=(0'aTc = 4/0 Z 2 _/60 100 (90 12 14. (15 points) Sketch the graph of the function f(a:) = Bil/(3:3 + 8). For this function, ":0 mafia"- N N N Decreasing: G h) *1) U (—1. , 0°) 1 n U n U 9.0»ch ~H—F— ewwmw a, ...
View Full Document

This note was uploaded on 02/07/2011 for the course MATH 135 taught by Professor Noone during the Spring '08 term at Rutgers.

Page1 / 11

2008 Calc Final s - PAM, 200% Pwm, (-3.ng 2 1. Find the...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online