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
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
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1e46184-5bb3-4339-852b-bb3ef2e0784b%2F1e938356-8b79-4a75-9dad-1b4e137467e9%2Fv2ouumi_processed.png&w=3840&q=75)
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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