Math 132 Midterm Examination 3 April 4 2012 6 multiple choice 4 long answer 100 points General Instructions Please answer the following without use of calculators You may refer to a 3x5 card but no other notes Part I of the exam is multiple choice while Part II is long answer Part I Instructions If you do not have a pencil to fill out your answer card please ask to borrow one from your proctor Write your Student ID number on the six blank lines on the top of your answer card and shade in the corresponding bubbles to the right of each digit Fill in the bubble corresponding to each of the following 6 questions Each is worth 4 points On Part I no partial credit will be given 1 The geometric series X 1 i 1 converges to 3i i 1 a 0 1 b 6 1 c 4 1 d 3 1 e 2 2 f 3 3 g 4 5 h 6 i 1 j Does not converge oscillates k Does not converge diverges to 2 Evaluate Z 8 0 1 dx 3 x a 0 b 1 c 2 d 3 e 4 f 5 g 6 h 7 i 8 j 16 k 3 Evaluate Z 1 4 x5 2 dx a b 0 1 c 20 1 d 12 1 e 3 1 f 2 2 g 3 3 h 4 5 i 4 j k Does not exist undefined diverges 4 Evaluate Z 2 2 1 dx x2 a 2 b 2 ln 2 c 1 d ln 2 e 0 f ln 2 g 1 h 2 ln 2 i 2 j Does not exist undefined diverges 5 Evaluate Z 2 sin 2 cos d 0 a 0 1 b 6 1 c 4 1 d 3 1 e 2 2 f 3 3 g 4 5 h 6 i 1 j 6 The sequence n4 converges as n to n a b 4 c 2 d 1 e 0 f 1 g 2 h 4 i j Does not exist undefined diverges Name Id Math 132 Part II Instructions Answer the following on the exam sheet showing all your work Correct answers without correct supporting work may not receive full credit You may use the back of each page for additional answer space please clearly indicate if you have done so or scratch work Please put your name and student id number on each page of Part II now 1 Exact evaluation of improper integrals and series a 6 points Evaluate X 2i i 1 3i 4i b 6 points For what values of x does X xi converge When it converges what i 0 does it converge to c 6 points Evaluate Z xe x dx 0 d 6 points Using partial fractions evaluate X 1 k 1 k 1 k 2 Name Id 2 Integration techniques a 6 points Evaluate b 6 points Evaluate c 6 points Evaluate d 5 points Evaluate Z z 4 dz z3 z Z 9x2 3x 6 dx x4 5x2 4 Z e3x dx 1 e2x Z 1 0 1 dx 3 x2 3 2 Math 132 Name Id 3 Series convergence Determine whether each of the following series converges or diverges a 6 points b 6 points X 2 i 1 i 2 i 1 3 i 1 i 2 X i 1 c 6 points X i3 2 1 sin2 i 2 i 1 i ln i Math 132 Name Id Math 132 4 Comparison tests for integrals Use a test for convergence for each problem on this page Don t try to find antiderivatives a 5 points Show that Z 1 b 5 points Show that Z 1 0 c 1 point Conclude that x2 1 dx converges x 1 dx converges x2 x Z 0 x2 1 dx converges x
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