test12004 - = 5 b Determine the radius of convergence of 1...

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Name±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± 5 February 2004 Teaching Assistant±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Hour Test 1 Math 1502C 10am Andrew Instructions: 1. Closed book. 2. Show your work and explain your answers and reasoning. 3. Calculators may be used, but pay particular attention to instruction 2. To receive credit, you must show your work. Unexplained answers, and answers not supported by the work you show, will not receive credit. 4. Express your answers in simplified form. 1. (25) Solve the initial value problem dy dt - 2 y = 4 t e 2 t y (0) = 5 2. (25) Evaluate the limits a. lim x 0 tan( x ) x + x 2 ˆ ˜ b. lim x x 2 e - x ( ) 3. (25) a. Determine the convergence/divergence of each of the series below. Be sure to state which convergence test you are using and to verify that its hypotheses are satisfied. i. k 2 5 k k = 0 ii. 1 k ln( k ) ( ) 2 k = 4 ii. 2 + sin( k ) k 2 k
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Unformatted text preview: = 5 b. Determine the radius of convergence of 1 k 2 k x-3 ( ) k k = 1 and determine whether this series converges when x = 6 and x = 4 . 4. (25) a. By computing a few derivatives, find the Taylor series for cos( x ) centered at 0. b. Use the "Alternating Series Estimate" to find the lowest degree partial sum a n x n n = N of your series in part a that approximates cos(1) to an accuracy of 10-3 . (You may assume the series does converge to cos(1).) Name±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± Page 2 of 2 Hour Test 1 Teaching Assistant±±±±±±±±±±±±±±±±±±±±±±±±±±±±±±± 5 February 2004 Answers 1. y = (2 t 2 + 5) e 2 t 2. a. 1 b. 3. a. All three series converge. b. R = 2. Converges at 4, diverges at 6. 4. a. (-1) k (2 k )! x 2 k k = b. 1 -x 2 2! + x 4 4!-x 6 6!...
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This note was uploaded on 09/07/2010 for the course CALC 1502 taught by Professor Morley during the Spring '08 term at Georgia Tech.

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test12004 - = 5 b Determine the radius of convergence of 1...

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