MAC 2312 Exam 3 Key

MAC 2312 Exam 3 Key - MAC 2312 Exam 3 Solutions July 26,...

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MAC 2312 Exam 3 Solutions July 26, 2011 Name: | {z } By writing my name, I swear by the honor code. Read all of the following information before starting the exam: Show all work, clearly and in order, if you want to get full credit. I reserve the right to take off points if I cannot see how you arrived at your answer (even if your final answer is correct). Circle or otherwise indicate your final answers. This test has 5 problems and is worth 50 points. It is your responsibility to make sure that you have all of the pages! Since time is limited, it is crucial that you think before you compute. You must state any theorems or tests that you use. All hypotheses must be verified. Good luck!
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1. Recall that if | x | < 1, then X n =0 x n = 1 1 - x . a) Find a power series representation for the function f ( x ) = 1 1 + x 2 . What is its radius of convergence? Solution: By the above, we have 1 1 + x 2 = 1 1 - ( - x 2 ) = X n =0 ( - x 2 ) n = X n =0 ( - 1) n x 2 n . This series is geometric and is convergent if |- x 2 | < 1, hence | x | < 1, so the radius of convergence is R = 1. b) Use part (a) to find the Maclaurin series for arctan x . What is its radius of convergence? (Hint: Recall that
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This note was uploaded on 10/13/2011 for the course MAC 2312 taught by Professor Bonner during the Summer '08 term at University of Florida.

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MAC 2312 Exam 3 Key - MAC 2312 Exam 3 Solutions July 26,...

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