03Final9C Sample

# 03Final9C Sample - University of California Riverside...

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University of California, Riverside Department of Mathematics Final Exam Mathematics 9C - First Year of Calculus Sample 3 Instructions: This exam has a total of 100 points. You have 3 hours. You must show all your work to receive full credit. You may use any result done in class. The points attached to each problem are indicated beside the problem. You are not allowed to use books, notes, or calculators. Answers should be written as p 2 as opposed to 1 : 4142135 ::: . 1. Which of the following sequences ( a n ) n ° 1 converges? Which diverges? Give reasons for your answers! (a) (5 points) a n = ° 1 + 1 2 n ± n (b) (5 points) a n = cos ( °n ) ° 1 + n n ± n 2. Consider the series 1 X n =2 ( ° 1) n p n (a) (5 points) Test if the series converges absolutely. Give reasons for your answer. (b) (5 points) Test if the series converges conditionally. Give reasons for your answer. 1

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3. (10 points) Test if the following series converges or diverges. Give reasons and clearly state if you are using any standard test.
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