Let f(z) be a function of period 27 such that 0, —7t Let f(x) be a function of period 27 such thatf(x) = {0,-T < x < 00 < x

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Let f(x) be a function of period 27 such that f(x) = { S 0, -T < x < 0 0 < x < T . a) Sketch a graph of f(x) in the interval –37 < x < 37 b) Show that the Fourier series for f(x) in the interval -T < x

Let f(x) be a function of period 27 such that f(x) = { S 0, -T < x < 0 0 < x < T . a) Sketch a graph of f(x) in the interval –37 < x < 37 b) Show that the Fourier series for f(x) in the interval -T < x

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 31E

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Question

Let f(z) be a function of period 27 such that 0, —7t

Let f(x) be a function of period 27 such that
f(x) = {
0,
-T < x < 0
0 < x <T .
x,
a) Sketch a graph of f(x) in the interval –3T < x < 37
b) Show that the Fourier series for f(x) in the interval -T <x < T is
1
cos 3x +
32
1
cos 5.x +
52
COS x +
...
4
1
sin 2x +
1
sin 3x
3
+ sin x
...
c) By giving appropriate values to x, show that
(1) 플 %=D 1-3+1- +
= 1-+- +...
and (i) 풍 3D1+ + + +..

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