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The Fourier series representation of the following function { X f(x + 4) = f(x) is f(x)≈1 - Σm=1 π² f(x) = -X cos((2m-1) Tx/2) (2m-1)² - 2 < x < 0, 0 ≤ x < 2;

The Fourier series representation of the following function { X f(x + 4) = f(x) is f(x)≈1 - Σm=1 π² f(x) = -X cos((2m-1) Tx/2) (2m-1)² - 2 < x < 0, 0 ≤ x < 2;

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 71E
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The Fourier series representation of the following function -X { 2² f(x + 4) = f(x) is 700 f(x)= =1+ + 3² = cos((2m-1)Tx/2) (2m-1)² f(x) ~1 - Σm=1 a State why (by using Fourier theorem) the Fourier series representation given above is a valid representation of f(x) on -2 < x < 2. - 2 < x < 0, 0 < x < 2; Show from the Fourier series representation given in part (a) that 1 Σm=1 (2m-1)². + =
Transcribed Image Text:The Fourier series representation of the following function -X { 2² f(x + 4) = f(x) is 700 f(x)= =1+ + 3² = cos((2m-1)Tx/2) (2m-1)² f(x) ~1 - Σm=1 a State why (by using Fourier theorem) the Fourier series representation given above is a valid representation of f(x) on -2 < x < 2. - 2 < x < 0, 0 < x < 2; Show from the Fourier series representation given in part (a) that 1 Σm=1 (2m-1)². + =
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