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2008 Calc Final s

2008 Calc Final s - PAM 200 Pwm-3.ng 2 1 Find the following...

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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': [email protected]+.)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, ...
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