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The Fourier series for the function f(x) = x, -T < x < T is sin nx E(-1)"-1. I-u 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 3 c) Use the integration theorem to show that %D n=1 6. COS nx 2 (7² – 3a?) = E(-1)"-1 -T < x < T n2 n=1

The Fourier series for the function f(x) = x, -T < x < T is sin nx E(-1)"-1. I-u 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 3 c) Use the integration theorem to show that %D n=1 6. COS nx 2 (7² – 3a?) = E(-1)"-1 -T < x < T n2 n=1

Advanced Engineering Mathematics
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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1. The Fourier series for the function f(x) = x, -T < x < n is E(-1)n-1 sin nx n n=1 a) Sketch the graph of the function fp which is the pointwise sum of the series on R. 1 b) Use Parseval's formula to show that n=1 72 c) Use the integration theorem to show that COS nx 2 (r² – 32²) = E(-1)"-1 -T < x < T n2 n=1 and 12 (7² – x²) = (-1)"-1sin næ п-1 -T < x < I n=1 d) Discuss whether the sum of each Fourier series in c) is piecewise continuous, continuous, piecewise Cl 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 < n is E(-1)n-1 sin nx n n=1 a) Sketch the graph of the function fp which is the pointwise sum of the series on R. 1 b) Use Parseval's formula to show that n=1 72 c) Use the integration theorem to show that COS nx 2 (r² – 32²) = E(-1)"-1 -T < x < T n2 n=1 and 12 (7² – x²) = (-1)"-1sin næ п-1 -T < x < I n=1 d) Discuss whether the sum of each Fourier series in c) is piecewise continuous, continuous, piecewise Cl or C1 on R. Sketch the graphs of the sum functions.
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