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1. Consider the function f defined by f(x) =| sin x |, for - T < x < T. a) Find the Fourier series of f. b) Sketch the graph of the function to which the series converges point- wise on R. Use the pointwise convergence theorem to justify your answer. c) By choosing a suitable value of x in the series that you have found, show that Ek=1 1 4k2 1

1. Consider the function f defined by f(x) =| sin x |, for - T < x < T. a) Find the Fourier series of f. b) Sketch the graph of the function to which the series converges point- wise on R. Use the pointwise convergence theorem to justify your answer. c) By choosing a suitable value of x in the series that you have found, show that Ek=1 1 4k2 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. Consider the function f defined by f(x) =| sin r |, for – T< x < T. a) Find the Fourier series of f. b) Sketch the graph of the function to which the series converges point- wise on R. Use the pointwise convergence theorem to justify your answer. c) By choosing a suitable value of x in the series that you have found, show that 2k=14k? 1 1
Transcribed Image Text:1. Consider the function f defined by f(x) =| sin r |, for – T< x < T. a) Find the Fourier series of f. b) Sketch the graph of the function to which the series converges point- wise on R. Use the pointwise convergence theorem to justify your answer. c) By choosing a suitable value of x in the series that you have found, show that 2k=14k? 1 1
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