math_172_(fall_2008)_(schumaker)_second_exam_(spring08)_(key)

Math_172_(fall_2008)_(schumaker)_second_exam_(spring08)_(key)

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Unformatted text preview: Math 172: Second Semester Calculus Spring Semester, 2008 Second Exam Name: ~ 1 Section: ID Number: Instru t'n- :Work must b hwn to receive or Question 1. (15 points) Let C be the curve (shown below) defined by y = cosx,— 7: s x s 7: . Write down, but do not evaluate, an integral that is equal to the arclength of C. Question 2. (15 points) An industriai-strength spring, obeying Hookes’ Law F(x) = kx, has a natural length of 1 meter. It takes 300 Joules of work to stretch the spring from 2 meter to 3 meters. Find the spring constant k and the amount of force F (in Newtons) required to hold the spring at 2 meters. =ww , natural 1611 L W; 45%de an! dirty“: beg/14d hafwa/ /Qny‘f/L Z Z [s _ 300 31m ~ f, AX c/x: 215%” : a/‘l l/utwl A :: é /?6€)) jWOd : 200 £231? ’ 4? M11202 Mfl p: Ax ; £0,771“): Zoo 1255 .. 260 442an Question 3. (20 points) ' d . Solve the differential equation '6; = Y3 511196, subject to the initial condition y(0) =1. 56, q/x'Va/f E]! ': fl/‘J /)r) (IX )1? / Mai/6N —Z = “(OJ/X) .. f’fioclx />/'3"y “' f m I Question 4. (15 points) Consider the geometric series: 5);? 3 le 3-44 2 3 gg‘jv/q’l //6 3 f4‘ 3" /9 7‘ (c) Determine the value of the series or show that it diverges. (Y/41 4 Pr 9 an 2: C 50 he AbuiagmHAMgm U‘ .- f % "/1 6 s _ 3 S m‘ //<§ 4/" f9 46’ +3 {7: +l44 4/? _I!6 Question 5. (7 points each) Consider the following series of positive terms. Use an appropriate test to determine whether they converge or diverge ahf GW‘San reff °°1+sin2(n) {+f;"2'/”) z = 5» — 0,, = (a) El n2/3 ht? )7 § 00 E; A" divergefi ,b- mm /}>=§< I) 1 {on drive/v39; (b) 2 2 lt‘m‘v‘ was», 724+ n=2 ’1 "n . [J - ,L an‘ ’72 £4 * 52—h flaw?“ ah g Amul‘ “.2 00 Q9 20» ' Z All Kohl/«wad #me 5:2 L’- //J:2 >/) [mi/f ém/ah'wn Terr fimé‘ 4r». Mch V Question 6. (7 points each) Determine, with justification, whether each of the following series is absolutely convergent, conditionally convergent, or divergent. . x ‘ 2 r (a) E n2+n [wt Q“ t [m hm : 5/ 450 "=1 (9”‘Dz ‘4 ’ w h” " my"; xa. +/ Mil/e472! 6R DVM90MC< (an) 3: .L hr.) (b) oZOZ(~1)n—1 2‘ [an] a [om/W7”)! P-Ruu "=1 "1'1 “3’ 1m! [P=I.I7l.) Em A fiémlufd.’ Wit) 76:7 002 [ailz/M'L aid—'1 in. (C) 6%, l 21,“ h) a h/ n=1 - j @ij/ .: _[ /h_il l :1 Z: “3:9 9» & LUZ: h/ 2. E: 90 I‘f 0450(Uél7 (“l/mafia . ...
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Math_172_(fall_2008)_(schumaker)_second_exam_(spring08)_(key)

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