2. For each of the following functions defined on the interval (0, 7): (a) Find the Fourier sine series. (b) Find the Fourier cosine series. (c) Sketch the functions to which the Fourier sine and cosine series con- verge on R. (i) f(x) = 2x – T (ii) f(x) = { 1 if 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. For each of the following functions defined on the interval (0, 7):
(a) Find the Fourier sine series.
(b) Find the Fourier cosine series.
(c) Sketch the functions to which the Fourier sine and cosine series con-
verge on R.
(i) f(x) = 2x
T
(ii) f(æ) = {
1 if 0<x <T/2
if T/2 < x < T
-1
(iii) f(x)
sin x.
Transcribed Image Text:2. For each of the following functions defined on the interval (0, 7): (a) Find the Fourier sine series. (b) Find the Fourier cosine series. (c) Sketch the functions to which the Fourier sine and cosine series con- verge on R. (i) f(x) = 2x T (ii) f(æ) = { 1 if 0<x <T/2 if T/2 < x < T -1 (iii) f(x) sin x.
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