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)?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
Question
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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