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(-1)"4"+1,n+1 3n+1(n + 1) In this problem, we investigate the power series n=0 Σ (-1)"4"+lpn+1 3n+1(n + 1) F(-1)"4"+1n+5 3n+1(n + 1) If we multiply the series by r we get r ,a re- n=0 n=0 4.x +1 lated power series, which is equal to r In 3 on the same interval you identified in part b. Express /a*im (+1). 4.x +1) dx as a power series in r. 3 x' In Let g(x) = x* In +1 Find g'(r), and the Maclaurin series for g'(x). 3 Consider, but do not give a response to the question: should you find the Maclaurin series for g'(x) directly, or by starting from the series in (c)?

(-1)"4"+1,n+1 3n+1(n + 1) In this problem, we investigate the power series n=0 Σ (-1)"4"+lpn+1 3n+1(n + 1) F(-1)"4"+1n+5 3n+1(n + 1) If we multiply the series by r we get r ,a re- n=0 n=0 4.x +1 lated power series, which is equal to r In 3 on the same interval you identified in part b. Express /a*im (+1). 4.x +1) dx as a power series in r. 3 x' In Let g(x) = x* In +1 Find g'(r), and the Maclaurin series for g'(x). 3 Consider, but do not give a response to the question: should you find the Maclaurin series for g'(x) directly, or by starting from the series in (c)?

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)"4"+1,n+1 3n+1(n + 1) In this problem, we investigate the power series n=0 Σ (-1)"4"+lpn+1 3n+1(n + 1) (-1)"4"+1pn+5 3n+1(n + 1) If we multiply the series by r we get r ,a re- n=0 n=0 4.x +1 lated power series, which is equal to r In 3 on the same interval you identified in part b. 4x +1) dx as a power series in x. 3 Express x' In 4x Let g(x) = x* In +1 Find g'(x), and the Maclaurin series for g'(x). 3 Consider, but do not give a response to the question: should you find the Maclaurin series for g'(x) directly, or by starting from the series in (c)?
Transcribed Image Text:(-1)"4"+1,n+1 3n+1(n + 1) In this problem, we investigate the power series n=0 Σ (-1)"4"+lpn+1 3n+1(n + 1) (-1)"4"+1pn+5 3n+1(n + 1) If we multiply the series by r we get r ,a re- n=0 n=0 4.x +1 lated power series, which is equal to r In 3 on the same interval you identified in part b. 4x +1) dx as a power series in x. 3 Express x' In 4x Let g(x) = x* In +1 Find g'(x), and the Maclaurin series for g'(x). 3 Consider, but do not give a response to the question: should you find the Maclaurin series for g'(x) directly, or by starting from the series in (c)?
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