Sol-162E2-S2009 - Spring 2009 MA 16200 Exam 2 1. Evaluate...

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Unformatted text preview: Spring 2009 MA 16200 Exam 2 1. Evaluate the integral: 2 / a32v4v—m2 dac . 7r/2 [f\ 741' ma x 2» S ivx . clfiilééél91£9’ 72; {CA/WA +: (LA/x i (EMA, :17; um Agfj::;fw NRA wévm E. 877 go )4 \/ (fa—ya" CM 3 8 @gm filesGM‘LcWfiLM/B D 07"”2'9‘7Dcé9' Lf £22” < "' ( M 9 1 1n|2+33| A‘ 5 1n|2_x|‘ C WM B. élan—m|—%1n|2+acl+0 M; :3 :2 W, 1 1 Chi (2%) (2w) l‘fik Zfiw C. 51n|2+m|—§1n]2—a3|+0 1 1 “9\$:A@HQ+E@#M Z 1n|2+ml —Zln|2—m|+0 wflmww r 27 ,_ V l E. i 1n|2—a:[—iln|2+w|+0 x3123“? ,\ ’3: f 0% “=5 A: '3 X152“? N: +LEB "9 T“ g; ( ( f” "wwwww ’ — .0 H WL, c. f ? ngG \ +L, w» + [MOAJA X +> x Lr kg . 1K1 L w [a]; Iggy) if?“ MA 16200 Exam 2 Spring 2009 3. The 'IYapezoidal Rule approximation of 1 /2 sin(m2)dm with n 2 3 0 is given by 1 1 1 f+wnnnwmmm , 1..., 1 . r 1 6(sin 02 + sin 62— + sin — A. 32 1 1 l 1 @E(sin02+28in6§+2sin§+sin§) i / I 1 62 32 t \ 1-?1 \ ‘ C. §(sin02+sin—l-+sin—}—+sin2i2) "’5 (gm? 1 “@4921 1 1'" H101 JngéfJ 1 . 2 . 1 . 1 . 1 D. E(23m0 +2s111~62—+231113—2+2s1n—2—2 1 . 2 , 1 , 1 , 1 E. E(s1n0 +2s1n6§+4s1n3—2+2s1n—2—2— 4. Which of the following is the most suitable substitution to evaluate the integral /\/6+a:2 da: Q+><Lwe XV-VWQ B. m=63e00 C. $=\/6S600 Z * 2 D.m=63in0 '3” 9" E. 3321/681116 : 0 Sale MA 16200 Exam 2 Spring 2009 5. Evaluate the integral below, if it converges /°° dm «3 :c(lnx)5 1 __ y 1% WE? ( A5 “’ €300 * (Q X) (gm B. 1 62%: 4 : 9:00 (“3; M \E E. Diverges : 0 + fiKQJZW H 1 —’ L!— ( Lt ) -‘ Ho 6. The form of the partial fraction decomposition for is L? A é+i'3+9—+ D +i+ F 'a: x2 $2+4 ($2+4)2 33—2 A Bx+0 Dan-FE F B.—— —---———— 933+ x2+4 +(m2+4)2+a:—2 @fl+£+£+Dm~l—E+ Fw+G + H m :02 2:3 3124—4 (3:2’+4)2 55—2 A B 0 Dm+E F D' §+Z£5+F+ m2+4 +m—2 E. £+Bx+C+Dm3+Em2+Fm+G+ H :03 1132+4 (m2+4:)2 93—2 MA 16200 Exam 2 Spring 2009 7. Find the length of the curve, 3,] : ln(cos cc), 0 3 ac _<_ 312$“) :JHW‘ 0- Inn/M2) : 3 gm, 3< gmcc sax >0 Dilnx/i {woifi—Efi. @ln(x/§+ 1) w“ W” H W” “7 ’“7 W 4 Wfiw‘ifi : j 4 H{ 5:35)” (iii 3 6 gab» AX 8. Which integral represents the area of the surface obtained by revolving the curve, y = 62‘”, 0 g a: g 1, about the y—axis? 1 A. / 27rcce2m da: 0 1 B. / 27rzm/ 1 + 643” d1: 0 «~ 1 27r03\/ 1 + 464$ do: 0 1 D. 271-629; V 1 + 6495 dx 0 E. 127re2$\/—1—-|Te4$ dm 1 Q Mm Amt. & zfi x / H'CLQM“) Afl MA 16200 Exam 2 Spring 2009 9. Which of the following represents the y—coordinate of the centroid of the bounded region bounded by y = sin 3:, y = 003$, :13 = 0, and w = 7741, where A is the area of the region? A 9 CD; x”? SPA? % ) 1 % 1 A. Z /0 §(coszw—sin2 x) dz: 1 % 1 . 2 2 B. A/O 2(sm :1: cos ac) dm vx @’ / x(cosaz—sina:) dm A 0 7r " D 1/3 (sinus cosm) dz): . —-- m __ A 0 A E- i/4 %m(cosm—sinm)2da: » x I n x > 0 w j 5% (cox-pat 137 I 7‘3: :1 A“ 4' ‘ ~91 3 A [Q A, O héos A A ,.., 00 2n 3'”. z i; = n=1 4 90 K 570 L in“ i 2:” in: Z 1(1) :21 C.3 (:94 :E‘Zdl‘ E. The series diverges. ' L V \ — 7/ 90 V\ 0” km ’3 M; 3 m ’3 ‘3 t u” “TA v m( w?) C 51"” 3 1:; I" 5; Li / 1 9 V\ l V\ ( ’11,, L{ «1’9 n K 3: 2“ if; W —/ 1 J73 \ ‘W‘ m ‘3— ; 1;. r 2 W “V ‘2— %W+Z w [+3 Ch é, a {nil h 3,11 5 MA 16200 Exam 2 11. Which of the following series converge? 0° 3711 ,r ,r , ' ‘ ' 3 I a" 7; 1+3n M‘ MWW #4 AW “My; m "’ 1 $49 b. :0: 1 ‘0 CL ‘ ‘45:“ l K ,4] Juggle» “fig/a ' W AW Z 7% wafer p oo VP?! 1 " A I ( C' :4; n(lnn)2 with P f 3 a? [I l 04’ 04‘ Z A. Only a. l A m j "E ( CM 2 74» V (g; "" clx. éOnlyb. Z XWAX} > ) 7\ Only c. v6 _Z;L _ a} { D. None ofthem. ’ a6“); [7/ X [4% v Hf “@xj E. All of them. y, xx : fli— ' B :: «ML-R 33> Mmen {:‘fiflo fit K2: QKL amt/mfg 12. Which of the following statements are true? I. If lanl = 0, then an 2 0 II. If i an converges, then an 2 0 n=1 III. If an'z 0, then i an converges. n=1 LC" ’lqwl 1": an (an! A. Ionly land II only ‘ («Q—<27) ilqwl 3” (Q ‘ lay/J 3‘0 o. I and 111 only =9 (@990 an :0 W7 gfiW—‘i‘tfi— W l D. II and III only fl 9.: “L N E. All of them. aU—t Z M flitgl :5) W3" 0Q r Z J1 W Mtg/21 941% L :9 61:1 V‘ wth w Spring 2009 ...
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This note was uploaded on 09/13/2011 for the course MATH 162 taught by Professor Petercook during the Fall '11 term at Purdue University-West Lafayette.

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Sol-162E2-S2009 - Spring 2009 MA 16200 Exam 2 1. Evaluate...

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