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+o0 Σ (-1)"(3n + 4) 23n+3 (n + 1) d. Differentiate f to determine the sum of the series n=0

+o0 Σ (-1)"(3n + 4) 23n+3 (n + 1) d. Differentiate f to determine the sum of the series n=0

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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Please provide complete solution. I'm trying to learn Power Series more in-depth. You don't need to answer A to C, only letter D is necessary. Thank you.

Let f(x) = x In(1+ x³). For all x E [-1, 1], it is known that +00 -1)" „n+1, In(1+x) = n +1 n=0 a. Find the Maclaurin series for f and identify its interval of convergence. b. Evaluate f(1804) (0), i.e., the 1804th derivative of f at x = 0. c. Use the 7th degree Maclaurin polynomial for f to approximate the value of 0.1 ln(1.001). (-1)"(Зп + 4) 23n+3(n + 1) d. Differentiate f to determine the sum of the series n=0
Transcribed Image Text:Let f(x) = x In(1+ x³). For all x E [-1, 1], it is known that +00 -1)" „n+1, In(1+x) = n +1 n=0 a. Find the Maclaurin series for f and identify its interval of convergence. b. Evaluate f(1804) (0), i.e., the 1804th derivative of f at x = 0. c. Use the 7th degree Maclaurin polynomial for f to approximate the value of 0.1 ln(1.001). (-1)"(Зп + 4) 23n+3(n + 1) d. Differentiate f to determine the sum of the series n=0
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