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Let f be the function defined for - ≤ x ≤ π by 1 0 f(x) if - π/2 ≤ x ≤ π/2 otherwise and then extended to be 27-periodic on the real number line. Part (a): Find the Fourier cosine series for this function. Part (b): Plot the first five terms of the series to see how well it approximates the function. (Us Mathematica or another tool to do this.)

Let f be the function defined for - ≤ x ≤ π by 1 0 f(x) if - π/2 ≤ x ≤ π/2 otherwise and then extended to be 27-periodic on the real number line. Part (a): Find the Fourier cosine series for this function. Part (b): Plot the first five terms of the series to see how well it approximates the function. (Us Mathematica or another tool to do this.)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 73E
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Let f be the function defined for -≤ x ≤ π by 1 f(x) = 0 and then extended to be 27-periodic on the real number line. Part (a): Find the Fourier cosine series for this function. Part (b): Plot the first five terms of the series to see how well it approximates the function. (Use Mathematica or another tool to do this.) Here is the plot of this function; it's a square wave. -3 -2 -1 0.8 0.6 0.4 0.2 if π/2 ≤ x ≤ π/2 otherwise 2 3
Transcribed Image Text:Let f be the function defined for -≤ x ≤ π by 1 f(x) = 0 and then extended to be 27-periodic on the real number line. Part (a): Find the Fourier cosine series for this function. Part (b): Plot the first five terms of the series to see how well it approximates the function. (Use Mathematica or another tool to do this.) Here is the plot of this function; it's a square wave. -3 -2 -1 0.8 0.6 0.4 0.2 if π/2 ≤ x ≤ π/2 otherwise 2 3
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