1. Let f(x) be a function of period 2n such that 1, -T

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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FOURIER SERIES

1.
Let f(x) be a function of period 27 such that
f(2) = { 0
1, -T <x < 0
0, 0<x< .
a) Sketch a graph of f(x) in the interval -2n < x < 2n
b) Show that the Fourier series for f(x) in the interval -T <x <T is
1
2
1
sin r + sin 3x +
1
sin 5x +
-
3
...
2
c) By giving an appropriate value to r, show that
1
1
1
+
3
1
4
7
Transcribed Image Text:1. Let f(x) be a function of period 27 such that f(2) = { 0 1, -T <x < 0 0, 0<x< . a) Sketch a graph of f(x) in the interval -2n < x < 2n b) Show that the Fourier series for f(x) in the interval -T <x <T is 1 2 1 sin r + sin 3x + 1 sin 5x + - 3 ... 2 c) By giving an appropriate value to r, show that 1 1 1 + 3 1 4 7
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