2. Consider periodic function [0, -

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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2. Consider periodic function
[0, -n<x<0
[x², 0<x<n
f(x)=<
a) Sketch graph y = f(x).
b) Obtain Fourier series representation for f(x).
c) Function f(x) has points of discontinuity which are finite. State the points and
what value of f(x) will converge at
those points of discontinuity.
d) Based on your answers in (b), show that
1 1 1
+
2² 3² 4²
dan
12
6
dan f(x+2) = f(x).
=1+
+ +
2² 32² 4²
4+
Transcribed Image Text:2. Consider periodic function [0, -n<x<0 [x², 0<x<n f(x)=< a) Sketch graph y = f(x). b) Obtain Fourier series representation for f(x). c) Function f(x) has points of discontinuity which are finite. State the points and what value of f(x) will converge at those points of discontinuity. d) Based on your answers in (b), show that 1 1 1 + 2² 3² 4² dan 12 6 dan f(x+2) = f(x). =1+ + + 2² 32² 4² 4+
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