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104S09makeupfinal - Math 104 Spring 2009 Final Exam...

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Unformatted text preview: Math 104 Spring 2009 Final Exam Make—up 1. Find the arc length of the curve y = flsinac + cos ac) for 0 g :c g g . all—i Mi c)\/§ d)1 e)? 2. Compute / :csin2xdx. o a)-% me e) +% d)%—% e)0 NI: 3. The base of a solid is the area between the curve 3/ = $2 , for 0 g {If g 1 , and the x—axis. The cross sections perpendicular to the w-axis are equilateral triangles. Find the area of this solid. 80% 19)1 0).; (1)3 6)? 2o 4. Find: flee 1—+1x2 dzr. a) g b) % 037” d) 7r e) diverges 5. Which of the following series converges: I 23 nsinz II z” 7%: III. 2:0 nsin %, a) None b) I and II C)I and 111 d) Only H e) All three 6. What is the interval of convergence of no: —+17L2 a)1<m<2 b)1§:c<2 c)1<:c§2 d)1§w§2 e)all:r. 7. The bounded region in the first quadrant between the curves y = x2 and y = 2 — as is rotated around the av— axis. Find the volume. £0271. b)3 7_7r (3)13; (1)9?” e) 327r_ 15 8. Compute the integral bl: / sin2 36 cos3 at day . 0 7 1 2 a) 60¢? b)12\/§ c)30 d) 40f e)0 9. The approximation 1 1 E E 24 is obtained from the first five terms of the MacLaurin expansion. From the Taylor remainder theorem, what is the guaranteed maximum absolute value of the error. (You may use e S 3.) a)§b)2174c)fil0 d)%e)%. 10. A certain medical study asserts that the number y of brain cells a person loses per day is related to the number of ounces :1: of alcohol consumed per day by the differential equation d g = 2xyln10. Assuming a person who does not drink alcohol loses 1000 brain cells per day, how much will a person who consumes two ounces of alcohol lose. a) 104 b) 105 c)106 d) 107 e) 108. 11. The third non-vanishing (i.e.non—zero) term in the MacLaurin expansion of the function $ f (w) = / (:os2tdt 0 is 5 3 4 a)0 b)’13—5 c)4i d)—% e)%. 12. The series w (—1)" Z % 1 71:2 71, a) converges absolutely b) diverges c) behavior cannot be determined d)converges conditionally e) would converge if the sum began with n = 3. 13. Determine the limit of the sequence if it exists. a) 0 b) 1 c)2 d) e e) does not exist. 14. Use Euler’s method with step size one to determine y(2) if y(0) = 1 and d?! 2 — : 2 . dxr “Cy a) O b) 1 (1)2 (1)3 e) 4. 15. The radius of converence of the series in 71:1 Nu (RC—2)” is a)0 b)% C); d); e)oo. 16. Find the total area of ther region bounded by the curves y : cc and y : 3:5 . a)0 b)% c)% d)§ e)1. 17. Solve the differential equation subject to the initial condition y(0) : 2. a) y=€% +1 b) y: (ew+7)i C)y= (6”+7)% d) y: (ex+31)% 6) y: (ex+15)%. 18. Compute the integral /2 dz .fi Vzc2—1. a) 1 b) ln;:£ c)ln\/1:+g d) 1H2" 2 e) 1112+”? 19. Compute the integral a) divergent b) 0 c)2ln2 d) —2ln2 e) %ln2. 20. Compute the integral /4 (1:1: 3 {CZ—ZT‘ 30% b) ingcg d) m; e) gm NICO Anwser Key 1.d 2.3 3.e 4.b 5.d 6.b 7.e 8.a 9.d 10.d 11.b 12.d 13.a 14.d 15.b 16.0 17.e 18.e 19.a 20.e ...
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