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(a) Find the Fourier series for the extended function. (b) Sketch the graph of f(x) as well as the function to which the series converges for three periods. (a) f(x): (b) f(m) = 0 1 if2< x < 0 0 < x < 2 if x + 1 if 1 < x < 0 (c) f(x) = 0 if 2

(a) Find the Fourier series for the extended function. (b) Sketch the graph of f(x) as well as the function to which the series converges for three periods. (a) f(x): (b) f(m) = 0 1 if2< x < 0 0 < x < 2 if x + 1 if 1 < x < 0 (c) f(x) = 0 if 2

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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4. In each of the problems, assume that the given function is periodically extended outside the original interval. (a) Find the Fourier series for the extended function. (b) Sketch the graph of f(x) as well as the function to which the series converges for three periods. (a) f(x) = = (b) f(x) = 0 1 if · 2 < x < 0 if 0 < x < 2 x+1 1 X if 1<x<0 if 0 < x < 1 - (c) ƒ(x) = = 0 X if - 2 < x < -1 if - 1<x< 1 1 < x < 2 0 if
Transcribed Image Text:4. In each of the problems, assume that the given function is periodically extended outside the original interval. (a) Find the Fourier series for the extended function. (b) Sketch the graph of f(x) as well as the function to which the series converges for three periods. (a) f(x) = = (b) f(x) = 0 1 if · 2 < x < 0 if 0 < x < 2 x+1 1 X if 1<x<0 if 0 < x < 1 - (c) ƒ(x) = = 0 X if - 2 < x < -1 if - 1<x< 1 1 < x < 2 0 if
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