2. Let f(x) be a function of period 27 such that f(r) = over the interval 0 < x < 2n. 2 a) Sketch a graph of f(x) in the interval 0 < x < 4n b) Show that the Fourier series for f(x) in the interval 0 < x < 2ñ is 1 sin x +, sin 2x + , sin 3x + 2 | c) By giving an appropriate value to x, show that 1 1 1 1 1 %D 4 5

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.5: Applications
Problem 28EQ
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FOURIER SERIES.

2.
Let f(x) be a function of period 27 such that
f(x) = 2
over the interval 0 < x < 2n.
a) Sketch a graph of f(x) in the interval 0 < x < 4m
b) Show that the Fourier series for f(x) in the interval 0 < x < 2ñ is
1
sin x + sin 2x + sin 3x +
2
c) By giving an appropriate value to x, show that
1
1
1
3
1
+
7
-
|
4
9.
+
Transcribed Image Text:2. Let f(x) be a function of period 27 such that f(x) = 2 over the interval 0 < x < 2n. a) Sketch a graph of f(x) in the interval 0 < x < 4m b) Show that the Fourier series for f(x) in the interval 0 < x < 2ñ is 1 sin x + sin 2x + sin 3x + 2 c) By giving an appropriate value to x, show that 1 1 1 3 1 + 7 - | 4 9. +
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