Consider the function - G with f(x + 4) = f(x). [a] Draw the graph of f(x) and also the graph of the function to which the Fourier series of f(x) converges on the interval [-6, 6]. f(x) = -2 < x < -1 x² -1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section: Chapter Questions
Problem 71RE
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Consider the function
10 -2<x<-1
-1 < x < 1
1<x<2
f(x) -
= x²
with f(x + 4) = f(x).
[a] Draw the graph of f(x) and also
the graph of the function to which
the Fourier series of f(x) converges
on the interval [-6, 6].
[b] Restate the function in part [a] in
the form of an odd or even function,
if possible. Find the Fourier series of
f(x) and simplify it as much as
possible.
[c] Use the obtained Fourier series to
evaluate the sum
n=0
Transcribed Image Text:Consider the function 10 -2<x<-1 -1 < x < 1 1<x<2 f(x) - = x² with f(x + 4) = f(x). [a] Draw the graph of f(x) and also the graph of the function to which the Fourier series of f(x) converges on the interval [-6, 6]. [b] Restate the function in part [a] in the form of an odd or even function, if possible. Find the Fourier series of f(x) and simplify it as much as possible. [c] Use the obtained Fourier series to evaluate the sum n=0
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