2)Given 0< x < f (x) = · 1 1 < 1 Find a) the Fourier cosine series expansion of f(x) b) the Fourier sine series expansion of f (x) cos5nx + 1 (cos2nx coSTX (Answer a: f(x) =- 2 cos3nx cos6TX cos10nx ... +.. 32 52 32 52 8 (1-2) sin2nx sin4nx +....) sinnx sin3пх (Answer b: f(x) = (1+2) 3n.

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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2)Given
1
0 <x <:
f(x) =
1
1
< 1
Find
a) the Fourier cosine series expansion of f(x)
b) the Fourier sine series expansion of f(x)
3
2
cos3nx
cos5nX
cos2nx
cos6nx
+
cos10nx
(Answer a: f(x) = -
coSTX
...
8
12
32
52
32
52
sin2nx
+
(1-)
sinnx
sin3пх sin4пх
(Answer b: f(x) = (1+2)
)+....)
Зл.
Transcribed Image Text:2)Given 1 0 <x <: f(x) = 1 1 < 1 Find a) the Fourier cosine series expansion of f(x) b) the Fourier sine series expansion of f(x) 3 2 cos3nx cos5nX cos2nx cos6nx + cos10nx (Answer a: f(x) = - coSTX ... 8 12 32 52 32 52 sin2nx + (1-) sinnx sin3пх sin4пх (Answer b: f(x) = (1+2) )+....) Зл.
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