Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Please JUST solve D! Thank you!
(A calculator is not allowed for this problem) The function f is defined by the power series (x-1)² (x-1)³ (x-1)4 2 3 4 (−1)″ −¹(x − 1)″ n f(x)=(x-1)- = ∞ Σ n=1 + for all real numbers x for which the series converges. +... (a) Determine the interval of convergence for f(x). Justify your answer. (b) Given g(x) = f'(x), find the first three terms and the general term of the power series for g(x). (c) Find a rational function that is identical to g(x) over its interval of convergence. (d) Let h(x) = f(x³+1). Find the closed form expression for (not an infinite series expression) h'(x). (HINT: use your result from part (c), .
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Transcribed Image Text:(A calculator is not allowed for this problem) The function f is defined by the power series (x-1)² (x-1)³ (x-1)4 2 3 4 (−1)″ −¹(x − 1)″ n f(x)=(x-1)- = ∞ Σ n=1 + for all real numbers x for which the series converges. +... (a) Determine the interval of convergence for f(x). Justify your answer. (b) Given g(x) = f'(x), find the first three terms and the general term of the power series for g(x). (c) Find a rational function that is identical to g(x) over its interval of convergence. (d) Let h(x) = f(x³+1). Find the closed form expression for (not an infinite series expression) h'(x). (HINT: use your result from part (c), .
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