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1. The periodic function f(x) has period 2. It is defined in the interval 0≤x≤ by f(x)=4x² (a) Sketch this function on the interval -4л≤x≤4л for the two cases i. f(x) is an odd function. ii. f(x) is an even function. (b) What can be deduced about the Fourier coefficients in these two cases? (c) Given that g(x): 4x², -

1. The periodic function f(x) has period 2. It is defined in the interval 0≤x≤ by f(x)=4x² (a) Sketch this function on the interval -4л≤x≤4л for the two cases i. f(x) is an odd function. ii. f(x) is an even function. (b) What can be deduced about the Fourier coefficients in these two cases? (c) Given that g(x): 4x², -

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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1. The periodic function f(x) has period 2. It is defined in the interval 0≤x≤ by f(x)=4x² (a) Sketch this function on the interval -4л≤x≤4л for the two cases i. f(x) is an odd function. ii. f(x) is an even function. (b) What can be deduced about the Fourier coefficients in these two cases? (c) Given that g(x): 4x², -<x≤0 [4x², 1, (≤x< is periodic function of period 27, by using integration by parts when required, calculate the Fourier coefficients for the function g(x), and express it as Fourier series expansion. (d) Hence deduce that π 47 12 Σ (−1)n+1 (n)2
Transcribed Image Text:1. The periodic function f(x) has period 2. It is defined in the interval 0≤x≤ by f(x)=4x² (a) Sketch this function on the interval -4л≤x≤4л for the two cases i. f(x) is an odd function. ii. f(x) is an even function. (b) What can be deduced about the Fourier coefficients in these two cases? (c) Given that g(x): 4x², -<x≤0 [4x², 1, (≤x< is periodic function of period 27, by using integration by parts when required, calculate the Fourier coefficients for the function g(x), and express it as Fourier series expansion. (d) Hence deduce that π 47 12 Σ (−1)n+1 (n)2
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