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math 160 spring 2009 exam 2002

math 160 spring 2009 exam 2002 - Points(48...

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Unformatted text preview: Points: (48 possible) (computed outof45) Name: ’20 llfit Q [1 5 Math 160 Spring 2009 Instructor: Jared Hersh Exam #2 Percent: _..——- Instructions: No outside notes allowed. You may use any type of calculator You may not use your cell-phone in lieu of a calculator and you may not share a calculator with a neighbor. Show all worldreasoning for every problem. Correct answers without supporting work will be treated with suspicion or as “lucky guesses" and will be scored accordingly. Any instances of cheating are taken very seriously by me and by SBCC; don‘t do it! Good luck® l. (5 points) Consider the curve y=2ln[sin-§], g'SxSn' b ‘1 J I, I l _ a) Set upanlntegral that would givethe length of this curve. 2 5 I (75) JJL a3l/j} b2?! 0‘ x -l . g; 23:..9; .(‘35(1_) 1, .- Jl Smelt.) P gilt!) 77 Ti .. * SW) J1 -: S (scl(—§)JJL -' )(5((33)y& -- L , 7- -11/.. fi/ I]; - 5 3 b) Evaluate this integral tofind the (exact) length of the curve. _ l T!“ "5?- W $1.13,. ,, 11~ M )csd’a‘wx : 28csc(u)c/u \ " ,7 TV X‘h/j r-au’fi/GJ }:?7 HM? L. 1) ”/6 2. (6 points, 2 each) a) Set up, but do not evaluate, an integral for the surface area obtained by rotating hecurvey=e’, 0<x$2,aboutthex-axis. ’J. 7—1. S = 2W3 1+5!“ «Jan =7- Szrre’fi/V 6 “- Gr 0—“; O _ ‘ a- 1 - 3;:e‘ 1. 1.3L b) Set up, but do not evaluate, an integral for the surface area obtained by rotating the curve y = e", 0 S x S 2 , about they-axis. S 2 thTTDL\/I+ fix J1 CL.- 41"!"— 0) Set up an integral that gives the same surface area as b), variable. (That is, if your integral from b) had a dx then with a dy, or vice-versa.) - 7. _. l- L 3261, oéié’l (‘3 1—2603; [fly—6 except with respect to the other you should now write down an integral ‘ “'3‘ - via 3- (5130ix1Is)EvaluateI 0? 2 Bi 1' 9’1 — SEC 6- mix +9 1‘11 3- r L31: 3f€£ 9 '_‘_ 8353(1'8 L16 ___._____‘___/. . 3+€M9r3j€L0 * i' 25:9 019 7351(009 ': i J9 %chc E; l V317; .. __ L C I ”i/UMSQ (0+9 9 --L -2 4 C ’37 3}“ W 7.. 4. (5 points) Talmte Ixfix (or show that it is divergent.) Use proper notation. _.. ' (ilk LC“ U't/an -j{m g JM‘ 0'1 {44:0 - 11‘” ' "f: l 3: ’1 r—a m: In 2, 11(- -’ UL: Inf In‘c - Jam {‘3 £440 “" fln'L M ) = m MM : Xw (/gn.;n(g}.—-/n (m) -{ 440 flnl {mo ”7/ GO . + ln-kgml if M 3 ...
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