3. Let the function f be defined by for -π < x < and satisfy f(x) = cosh x f(x + 2π) = f(x). Recall that cosh x = (e* + e*)/2 and in the following you are given the indefinite integral Scc cosh(ax) cos(bx) dx = 1 a² + b² (a sinh(ax) cos(bx) + bcosh(ax) sin(bx)) for constants a and b. (a) Sketch the graph of this function for -37 < x < 3π. (b) Find the Fourier series for f(x).

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
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3. Let the function f be defined by
for - < x < and satisfy
f(x) = cosh x
f(x + 2π) = f(x).
Recall that cosh x = (e* + e*)/2 and in the following you are given the indefinite integral
Sco
cosh(ax) cos(bx)dx=
1
a² + b²
(a sinh(ax) cos(bx) + b cosh(ax) sin(bx))
for constants a and b.
(a) Sketch the graph of this function for -37 < x < 3π.
(b) Find the Fourier series for f(x).
Transcribed Image Text:3. Let the function f be defined by for - < x < and satisfy f(x) = cosh x f(x + 2π) = f(x). Recall that cosh x = (e* + e*)/2 and in the following you are given the indefinite integral Sco cosh(ax) cos(bx)dx= 1 a² + b² (a sinh(ax) cos(bx) + b cosh(ax) sin(bx)) for constants a and b. (a) Sketch the graph of this function for -37 < x < 3π. (b) Find the Fourier series for f(x).
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