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f(x)=sinh(x)= n 2n+1 (2n+1)! =x+ + f +³ + +. 3! 5! 7!

f(x)=sinh(x)= n 2n+1 (2n+1)! =x+ + f +³ + +. 3! 5! 7!

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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5. f(x)=sinh(x)= 20+1 + +... Notice that f(x) is an odd function. (2n+1)! 3! 5! 7! +³ =x+ (a) What happens to the value of f(x) as x increases? (b) Looking at the terms in the series, what is the minimum value of f'(x)? (c) Show that when performing the Ratio Test, we get L = lim 11-00 (d) What is the interval of convergence for f(x) = sinh(x)? (e) Write a series for g(x)=x-sinh(x³). (2n+3)(2n+2)
Transcribed Image Text:5. f(x)=sinh(x)= 20+1 + +... Notice that f(x) is an odd function. (2n+1)! 3! 5! 7! +³ =x+ (a) What happens to the value of f(x) as x increases? (b) Looking at the terms in the series, what is the minimum value of f'(x)? (c) Show that when performing the Ratio Test, we get L = lim 11-00 (d) What is the interval of convergence for f(x) = sinh(x)? (e) Write a series for g(x)=x-sinh(x³). (2n+3)(2n+2)
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