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for all x E R. n! n=0 Consider e" = a. Determine the power series representation of f(x) = xe-5æ for all x E R. b. By first differentiating the power series in (a), determine the exact value (-1)*+1(2n + 1) n! n=0 c. Find f(23) (0). No need to simplify your answer.

for all x E R. n! n=0 Consider e" = a. Determine the power series representation of f(x) = xe-5æ for all x E R. b. By first differentiating the power series in (a), determine the exact value (-1)*+1(2n + 1) n! n=0 c. Find f(23) (0). No need to simplify your answer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Consider et for all x E R. n! n=0 -5x2 a. Determine the power series representation of f(x) = xe' for all x E R. b. By first differentiating the power series in (a), determine the exact value of -1) n+1(2n + 1) n! n=0 c. Find f(23) (0). No need to simplify your answer.
Transcribed Image Text:1. Consider et for all x E R. n! n=0 -5x2 a. Determine the power series representation of f(x) = xe' for all x E R. b. By first differentiating the power series in (a), determine the exact value of -1) n+1(2n + 1) n! n=0 c. Find f(23) (0). No need to simplify your answer.
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