real analysis 3. For x ≥ 0, letf(x) = ² lolog(1+t) dt.t(a) Prove that the Taylor series for f about 0 is89(x) = (-1)^+12.nn²n=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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Answered: 3. For x ≥ 0, let I f(x) = f* log(1 +t)…

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 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.