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3. For x ≥ 0, let I f(x) = f* log(1 +t) dt. t (a) Prove that the Taylor series for f about 0 is 8 [² g(x) = Σ n=1 (−1)n+1pn n² (b) For what x is g(x) = f(x)? Justify your answer. (c) For what x is g'(x) = log(1+x)/x? Justify your answer.

3. For x ≥ 0, let I f(x) = f* log(1 +t) dt. t (a) Prove that the Taylor series for f about 0 is 8 [² g(x) = Σ n=1 (−1)n+1pn n² (b) For what x is g(x) = f(x)? Justify your answer. (c) For what x is g'(x) = log(1+x)/x? Justify 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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3. For x ≥ 0, let f(x) = ² lo log(1+t) dt. t (a) Prove that the Taylor series for f about 0 is 8 9(x) = (-1)^+12.n n² n=1 (b) For what x is g(x) = f(x)? Justify your answer. (c) For what x is g'(x) = log(1+x)/x? Justify your answer.
Transcribed Image Text:3. For x ≥ 0, let f(x) = ² lo log(1+t) dt. t (a) Prove that the Taylor series for f about 0 is 8 9(x) = (-1)^+12.n n² n=1 (b) For what x is g(x) = f(x)? Justify your answer. (c) For what x is g'(x) = log(1+x)/x? Justify your answer.
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