Exercises 2 Let f(x) be a function of period 27 such that 0 < x < T T < x < 2T TT - x, f (1x) = { 0, 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 0 < x < 27 is + 4 1 cos 3x + 32 Cos 5x + 52 COS x + 1 sin 4.x +... sin x + sin 2x + sin 3x + 3 c) By giving an appropriate value to x, show that 1 = 1+ 32 1 ... 8 52
Exercises 2 Let f(x) be a function of period 27 such that 0 < x < T T < x < 2T TT - x, f (1x) = { 0, 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 0 < x < 27 is + 4 1 cos 3x + 32 Cos 5x + 52 COS x + 1 sin 4.x +... sin x + sin 2x + sin 3x + 3 c) By giving an appropriate value to x, show that 1 = 1+ 32 1 ... 8 52
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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Transcribed Image Text:Exercises 2
Let f(x) be a function of period 27 such that
f (x) = {
={"
0 < x < T
T < x < 2n
TT - x,
0,
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 0 < x < 2n is
1
cos 3x +
32
Cos 5x +
52
COS x +
4
1
sin 4x +. ..
sin x +
sin 2x +
sin 3x +
3
c) By giving an appropriate value to x, show that
1
= 1+
32
1
...
52
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