Thomas' Calculus: Early Transcendentals

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Unformatted text preview: Name W 1. Evaluate /(62 + 1) costH. Helm 004.9099 = [91mfidéw Imam £1,531,049) ’0': M9) A") Name 3. Evaluate / V332 — l 3:2 dm. Hint: you may at some point want to use sin2 6’ = 1 — C082 09. Name Nz-l = JAeJOH ”17‘7““? W Jifwf )t—MB WMIS’iB ff M29 Name 0° sin2 :1: , , 4. Does d3: converge or dlverge? lee your reasons. 0 IE2 WW - “AW . ‘7- l -7_ W7%I,MM"~)IWMQ§ MIX/Ly X x1 0 Y Name 5. For each of the following three series, state Whether it converges or diverges and give your reasons. 00771-2” ‘ . a) 2 (2w. WW WWW. ~ wWWfi 53;" web; W [email protected]“)\ N ame 6. For what values of :6 does each of the following two series converge? Give your reasons. Wt \fl 7L” ” (“3' leri an. M. —‘> ”3 W M 3 X=0 MW 2 (:%)WV£ W Name 7 . Find the second order Taylor polynomial of tam‘1 :6 about the center a = % Name 8. Find 3/101 with an error at most 0.0001. Hint: 3/10 2 (1 + 0.01)1/3. @{[x)3(1+7‘)"g New”) WW“W‘ Name 9. a) Draw the graph of the first two turns of the spiral given in polar coordinates by r = 26 (that is, for 0 g 6 g 471'). b) Find the area of the region enclosed between the first and second turn of the spiral (i.e., the region between the curves 7" :: 26 for 0 g 9 g 27r and 7“ 2 20 for 27r S 0 3 471', as well as the positive {Is—axis between 0 and 471'). 1m 2.,r A] —% (133749” imitate 11f _ hr ‘1 9 ’9‘ 1119 fie .. 3., 93]“ > 3.. (ha—21.813: Egg-”5 “ a 1* 3 3 3 H Name 10. Find all real or complex solutions to 28 — 24 —— 2 z 0. Name 11. The region inside the curve $2 y2 _ __:1 9+4 and above the m-axis is revolved about the x-axis. Find the volume. Name 12. Solve the initial value problem dy 3 ——~2: 1:. wdm y 9:8 M) 0 aOMoQ 3} 76 : &.3 3X28} M X V‘M/LM/vw WWW Pfi):‘;)QW'—k2x'c ...
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