Consider e": for all æ E R. n! a. Determine the power series representation of f(x) = xe-5x² for all x € R. b. By first differentiating the power series in (a), determine the exact value of 은 (-1)까1(2n+ 1) n! n=0 c. Find f(23) (0). No need to simplify your answer.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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1. Consider e" =
), for all x E R.
a. Determine the power series representation of f(x) = xe-5a² for all x E R.
b. By first differentiating the power series in (a), determine the exact value of
(-1)"+1(2n + 1)
n!
n=0
c. Find f(23)(0). No need to simplify your answer.
Transcribed Image Text:1. Consider e" = ), for all x E R. a. Determine the power series representation of f(x) = xe-5a² for all x E R. b. By first differentiating the power series in (a), determine the exact value of (-1)"+1(2n + 1) n! n=0 c. Find f(23)(0). No need to simplify your answer.
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