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Find the Maclaurin series for f and identify its interval of convergence. Evaluate f(1804) (0), i.e., the 1804th derivative of f at æ = 0. Use the 7th degree Maclaurin polynomial for f to approximate the value of 0.1 ln(1.001). (-1)"(Зп + 4) Differentiate f to determine the sum of the series 23n+3(п + 1) n=0 W!

Find the Maclaurin series for f and identify its interval of convergence. Evaluate f(1804) (0), i.e., the 1804th derivative of f at æ = 0. Use the 7th degree Maclaurin polynomial for f to approximate the value of 0.1 ln(1.001). (-1)"(Зп + 4) Differentiate f to determine the sum of the series 23n+3(п + 1) n=0 W!

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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Let f(x) = x ln(1+x*). For allx € (-1,1), it is known that Σ +oo (-1)" -7n+1 n +1 In(1+x) n=0 1. Find the Maclaurin series for f and identify its interval of convergence. 2. Evaluate f(1804) (0), i.e., the 1804th derivative of f at x = 0. 3. Use the 7th degree Maclaurin polynomial for f to approximate the value of 0.1 ln(1.001). +o0 (-1)"(3п + 4) 23n+3 (n + 1) 4. Differentiate f to determine the sum of the series n=0
Transcribed Image Text:Let f(x) = x ln(1+x*). For allx € (-1,1), it is known that Σ +oo (-1)" -7n+1 n +1 In(1+x) n=0 1. Find the Maclaurin series for f and identify its interval of convergence. 2. Evaluate f(1804) (0), i.e., the 1804th derivative of f at x = 0. 3. Use the 7th degree Maclaurin polynomial for f to approximate the value of 0.1 ln(1.001). +o0 (-1)"(3п + 4) 23n+3 (n + 1) 4. Differentiate f to determine the sum of the series n=0
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