Math 132 Spring 2009 Exam 2 NAME STUDENT ID NUMBER This exam contains sixteen questions The first fourteen are multiple choice questions and count for five points each There is no partial credit on these questions so read each question carefully check your arithmetic and make sure that you have marked the answer you intended to mark The last two questions which are each worth fifteen points require written answers and some partial credit might be given However no credit will be given for information that is not germane to the problem at hand Please make sure to write your name and student ID number on the pages that include your answers to the last two questions In fact you will get one point on each of these two questions for writing your name and ID number legibly 1 1 Expand a b c d e f g x 4 x 1 2 1 x 1 2 x 1 3 x 1 4 x 1 1 x 1 3 x 1 3 x 1 2 by partial fractions x 3 x 1 2 x 2 x 1 2 x 1 x 1 2 x x 1 2 3 x 1 2 h impossible since undefined at x 1 2 2 Compute Z 4 2 2x3 2x2 1 x2 x a 12 ln 2 3 b 16 ln 4 c 16 ln 4 ln 3 d 16 ln 4 3 e 16 ln 3 4 f g h 32 3 3 Which term does NOT appear in the partial fractions expansion of x8 3x7 20x5 13x3 x2 x 7 x2 x 1 4 x4 1 a A x2 b B x 1 4 C x 1 5 D x Ex F x2 1 Gx H x2 1 J x 1 K x 1 3 c d e f g h 4 4 Use the Trapezoidal Rule with n 4 to approximate R2 2 x x dx 0 a 0 41 b 0 86 c 1 27 d 1 55 e 2 31 f 2 72 g 3 33 h 3 54 5 5 Use Simpson s Rule with n 4 to approximate a 0 86 b 1 32 c 2 75 d 3 38 e 3 45 f 3 54 g 4 27 h 4 34 6 R2 2 x 0 x dx 6 Find the minimum number of subintervals needed to R 2 approximate 01 ex dx with an error less than 10 4 when using the Trapezoidal Rule a 4 b 50 c 63 d 117 e 189 f 224 g 451 h 1003 7 7 Evaluate R 11 10 dx 1 x a 2 b 10 c 25 d 110 e 1100 f 1250 g h 8 8 Evaluate Z 2 1 dx ln x a Converges by direct comparison with comparison function x12 b Diverges by direct comparison with the comparison function x12 c Converges by direct comparison with the comparison function ex d Diverges by direct comparison with the comparison function ex e Converges by direct comparison with the comparison function x1 f Diverges by direct comparison with the comparison function x1 g Converges by direct comparison with the comparison function e x h Diverges by direct comparison with the comparison function e x 9 9 Evaluate Z 1 dx e2x x2 a Converges by limit comparison with the comparison function x1 b Diverges by limit comparison with the comparison function x1 c Converges by limit comparison with the comparison function e1x d Diverges by limit comparison with the comparison function e1x e Converges by direct comparison with comparison function x1 f Diverges by direct comparison with the comparison function x1 g Converges by direct comparison with the comparison function e1x h Diverges by direct comparison with the comparison function e1x 10 10 Evaluate Z 2 0 dx x 1 a Diverges to b Diverges to c Diverges but not to or d 0 e 1 f 1 g 2 h 2 11 11 The region between the curve y 2 x 0 x 1 and the x axis is revolved about the x axis to generate a solid Compute the volume of this solid a 2 b c 2 d 5 2 e 5 f 2 g 2 2 h 16 15 12 12 Find the volume of the solid generated by revolving the region bounded by y x and y 1 about the x axis a 4 3 b c 2 d 5 2 e 5 f 2 g 2 2 h 6 3 13 13 Find the volume of the solid generated by revolving the region between x y 2 1 and the line x 2 about the line x 2 a 2 b c 2 d 5 2 e 5 f 2 g 2 2 h 16 15 14 14 Find the length of the curve given by y x3 2 0 x 4 3 a 2 3 b 4 3 c 8 3 d 8 27 e 9 4 f 13 4 g 56 27 h 128 27 15 Name Student ID 15 Use the shell method to find the volume of the solid generated by revolving the region bounded by y 1 x2 4 0 x 1 and the x axis about the line x 1 16 Name Student ID 16 Find the length of the curve given by x cos3 t y sin3 t 0 t 2 17 Name Student ID 18 Name Student ID 19
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