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The Fourier series for the function f(x) = x, -T < x < T is sin nx E(-1)"-1; n n=1 a) Sketch the graph of the function fp which is the pointwise sum of the series on R. b) Use Parseval's formula to show that = 5. c) Use the integration theorem to show that 2 (7? – 3a²) = E(-1)"-108 næ -T < x < T n2 n=1 and n*(r² – x²) = E(-1)"-1 sin næ -T < x

The Fourier series for the function f(x) = x, -T < x < T is sin nx E(-1)"-1; n n=1 a) Sketch the graph of the function fp which is the pointwise sum of the series on R. b) Use Parseval's formula to show that = 5. c) Use the integration theorem to show that 2 (7? – 3a²) = E(-1)"-108 næ -T < x < T n2 n=1 and n*(r² – x²) = E(-1)"-1 sin næ -T < x

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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1. The Fourier series for the function f(x) = ;x, –T < x < r is sin nx n n=1 a) Sketch the graph of the function fp which is the pointwise sum of the series on R. b) Use Parseval's formula to show that E = . n=1 c) Use the integration theorem to show that COS nx (7? – 30²) = E(-1)"-1 n2 -T < x < T n=1 and sin nx * (r² – a²) = E(-1)"-1; -T < x < T n3 n=1 d) Discuss whether the sum of each Fourier series in c) is piecewise continuous, continuous, piecewise C1 or C1 on R. Sketch the graphs of the sum functions.
Transcribed Image Text:1. The Fourier series for the function f(x) = ;x, –T < x < r is sin nx n n=1 a) Sketch the graph of the function fp which is the pointwise sum of the series on R. b) Use Parseval's formula to show that E = . n=1 c) Use the integration theorem to show that COS nx (7? – 30²) = E(-1)"-1 n2 -T < x < T n=1 and sin nx * (r² – a²) = E(-1)"-1; -T < x < T n3 n=1 d) Discuss whether the sum of each Fourier series in c) is piecewise continuous, continuous, piecewise C1 or C1 on R. Sketch the graphs of the sum functions.
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