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Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter6: The Trigonometric Functions

Section6.6: Additional Trigonometric Graphs

Problem 77E

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1. The periodic function f(x) has period 2. It is defined in the interval 0≤x≤ by
f(x)=4x²
(a) Sketch this function on the interval -4л≤x≤4л for the two cases
i. f(x) is an odd function.
ii. f(x) is an even function.
(b) What can be deduced about the Fourier coefficients in these two cases?
(c) Given that
g(x):
4x², -<x≤0
[4x²,
1,
(≤x<
is periodic function of period 27, by using integration by parts when required, calculate
the Fourier coefficients for the function g(x), and express it as Fourier series expansion.
(d) Hence deduce that
π
47
12
Σ
(−1)n+1
(n)2

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1. The periodic function f(x) has period 27. It is defined in the interval 0≤x≤ by f(x) = 2x² (a) Sketch this function on the interval -47 ≤x≤ 47 for the two cases i. f(x) is an odd function. ii. f(x) is an even function. (b) What can be deduced about the Fourier coefficients in these two cases?
I did this problem with the help of a previous solution, but it was marked incorrect. Could you please see where it might have gone wrong?
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