ser. the etermined by f(x) = x² for x = [-π, π] and f(x+2) = f(x) for all € R and using facts considered in lecture, explain why the Fourier ries coverges to f(x) at each point x = (-7, 7). ) Using the Fourier series representation from part (a), evaluate =(-1)" (−1)n n² =1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
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Please do b and please do not type the answer
(a) Find the Fourier series for the function f: R → R
determined by f(x) = x² for x = [-π, π] and f(x + 2) = f(x) for all
x = R and using facts considered in lecture, explain why the Fourier
series coverges to f(x) at each point x = (-π, π).
(b) Using the Fourier series representation from part (a), evaluate
∞
(-1)"
n²
n=1
Transcribed Image Text:(a) Find the Fourier series for the function f: R → R determined by f(x) = x² for x = [-π, π] and f(x + 2) = f(x) for all x = R and using facts considered in lecture, explain why the Fourier series coverges to f(x) at each point x = (-π, π). (b) Using the Fourier series representation from part (a), evaluate ∞ (-1)" n² n=1
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