Math 132 Spring 2011 Exam 1 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 Compute Z2 1 a 2 3 b 3 2 c 1 2 d 1 4 e 3 4 f 3 4 g 0 h 1 2 2 1 dx x2 2 Find an antiderivative of f t 1 a 2 C t b c d 1 C 2 t 12 t3 2 12 t3 2 C e 2 t 5 f 2 t 5 g 12 t h 21 t 3 1 t 3 Suppose f is a function such that f 0 10 f 0 0 22 f 00 0 2 f 4 1 f 0 4 20 f 00 4 30 Compute Z4 f 00 t dt 0 a 9 b 2 c 28 d 12 e 10 f 1 g 8 h 18 4 4 Compute Z4 1 3r 1 dr r a 12 b 3 c 2 d e 2 3 1 2 f 14 g 3 h 21 5 5 A table of values for an increasing function g is shown x 10 15 20 25 30 g x 4 2 0 1 11 Use this table to find lower and upper estimates for Z30 g x dx 10 a 4 10 b 2 20 c 0 30 d 6 100 e 6 100 f 5 70 g 6 70 h 25 50 6 6 Suppose g y Zy t10 sint dt 2 0 Compute g y a y 10 siny b y 10 cosy c y 10 cosy d 9y siny y 10 cosy e 9y siny y 10 cosy f 9y siny y 10 cosy 2 g 9y siny y 10 cosy 4sin2 h 9y siny y 10 cosy C 7 7 Suppose h x Z 1 sec t dt x Compute h0 x a b c 1 sec t d 1 sec x e 1 sec t f 1 sec x g 1 sec 1 sec x h 1 sec 1 sec x C 8 8 Compute dx x lnx Z a cos ex C b ecos x C c x sin ex C d ln x C e ln x C f 1 ln x C g ln ln x C h 1 x C 9 9 Compute Z 1 z 2 1 2z 3 5 dz 0 a 1 6 b 61 c 1 36 1 d 36 e 1 3 1 f 18 g 0 h 91 10 10 Evaluate Ze 9x2 ln x dx 1 a 0 b 1 2e3 c 1 2 d e 1 e 9e3 f 3e2 g 2 e2 h 32 e 11 11 Compute Z 0 a 4 1 cos4x dx 4 b 0 c 1 d e 2 2 2 f 2 g 4 h 0 25 12 12 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 13 13 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 Gx H x2 1 C x 1 5 D x Ex F x2 1 J x 1 K x 1 3 c d e f g h 14 14 Compute Z1 0 1 dx x2 1 3 a 0 b 3 c 4 d 2 e 2 2 f 2 2 g 1 2 h 1 2 15 Name Student ID 15 Evaluate Z et sin 2t dt Show your work 16 Name Student ID 16 Compute limn n X i 1 Show all work 17 2 1 1 i n 2 n Name Student ID 18 Name Student ID 19 Name Student ID 20
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