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

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

This preview shows pages 1–6. Sign up to view the full content.

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 . ...
View Full Document

This note was uploaded on 02/14/2011 for the course MATH 172 taught by Professor Remaley during the Spring '10 term at Washington State University .

Page1 / 6

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

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online