f(x)= duce that 1 ere f(x+2n)=f(x). d the Fourier series for the function f(x)= for -

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.7: Operations On Functions
Problem 55E
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1. Find the Fourier series of the function
{}
1
f(x)=
where f(x+2n)=f(x).
2. Find the Fourier series for the function
Deduce that
f(x)=
T
I
4
for -<x<0
for 0<x<*
H.W.
and f(n)=f(0) =f(n)=0,
Л 1 1 1
== --+---+...
4 357
Ans.
1
inx+in+sn,xnx..
1 1
3x+-sin 5x+-sin
x+sin
5
41
T1
for -<x<0
for 0<x<*
sinx+-sin
3
f(x)=f(x+2n) for all x.
sinx sin 3x sin 5x
Ans. ·+·
1 3 5
sin 7.x
7
7x+.
7.x:
Transcribed Image Text:1. Find the Fourier series of the function {} 1 f(x)= where f(x+2n)=f(x). 2. Find the Fourier series for the function Deduce that f(x)= T I 4 for -<x<0 for 0<x<* H.W. and f(n)=f(0) =f(n)=0, Л 1 1 1 == --+---+... 4 357 Ans. 1 inx+in+sn,xnx.. 1 1 3x+-sin 5x+-sin x+sin 5 41 T1 for -<x<0 for 0<x<* sinx+-sin 3 f(x)=f(x+2n) for all x. sinx sin 3x sin 5x Ans. ·+· 1 3 5 sin 7.x 7 7x+. 7.x:
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