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Unformatted text preview: Math 242 Homework 10 Solutions 1. Express the indefinite integral Z e x 1 x dx as a power series. e x = 1 + x 1! + x 2 2! + x 3 3! + x 4 4! + Â·Â·Â· = âˆž X n =0 x n n ! e x 1 = x 1! + x 2 2! + x 3 3! + x 4 4! + Â·Â·Â· = âˆž X n =1 x n n ! e x 1 x = 1 1! + x 2! + x 2 3! + x 3 4! + Â·Â·Â· = âˆž X n =1 x n 1 n ! Z e x 1 x dx = x 1 Â· 1! + x 2 2 Â· 2! + x 3 3 Â· 3! + x 4 4 Â· 4! + Â·Â·Â· = âˆž X n =1 x n n Â· n ! 2. Express the definite integral Z . 2 1 1 + x 5 dx as an infinite series. Then find the sum of the first two terms of that series. Compare that to the value of the integral that Maple gives you. 1 1 1 x = 1 + x + x 2 + x 3 + Â·Â·Â· = âˆž X n =0 x n 1 1 + x = 1 x + x 2 x 3 + Â·Â·Â· = âˆž X n =0 ( 1) n x n 1 1 + x 5 = 1 x 5 + x 10 x 15 + Â·Â·Â· = âˆž X n =0 ( 1) n x 5 n Z . 2 1 1 + x 5 dx = Z . 2 1 x 5 + x 10 x 15 + Â·Â·Â· dx = x x 6 6 + x 11 11 x 16 16 + Â·Â·Â· . 2 = 0 . 2 (0 . 2) 6 6 + (0 . 2) 11 11 (0 . 2) 16 16 + Â·Â·Â· = âˆž X n =0 ( 1) n (0 . 2) 5 n +1 5 n...
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This note was uploaded on 12/07/2011 for the course MATH 242 taught by Professor Wang during the Spring '08 term at University of Delaware.
 Spring '08
 wang
 Power Series

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