Exercise 4. Consider the following function f(x) = 2|x| if -л≤ x ≤π, extended to the entire real line as a periodic function with period 2. (a) (5 points) Sketch a graph of ƒ on the real line. (b) (30 points) Calculate the Fourier series of f. (c) (5 points) For which values of x = R does the value of the Fourier series of f coincide with f(x)?
Exercise 4. Consider the following function f(x) = 2|x| if -л≤ x ≤π, extended to the entire real line as a periodic function with period 2. (a) (5 points) Sketch a graph of ƒ on the real line. (b) (30 points) Calculate the Fourier series of f. (c) (5 points) For which values of x = R does the value of the Fourier series of f coincide with f(x)?
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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Transcribed Image Text:Exercise 4. Consider the following function
f(x) = 2|x| if -л≤ x ≤π,
extended to the entire real line as a periodic function with period 2.
(a) (5 points) Sketch a graph of ƒ on the real line.
(b) (30 points) Calculate the Fourier series of f.
(c) (5 points) For which values of x = R does the value of the Fourier series of f coincide with f(x)?
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