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Suppose we have a periodic function f with period 2, defined on z € [-1, 1] by: The Fourier series of f is given by: NB: In this question you will need to simplify cos(n) and sin(n) by exploiting that n is an integer. In the Fourier series of f, what is the value of ag? In the Fourier series of f, what is the value of an for n € N? In the Fourier series of f, what is the value of the b for n € N? Check 0 -1 -2 -3 -4 -0.5 0 1 € (-1,0], T € (0, 1]. 0.5 F(x)= ao+an cos( n 1) + b₂ sin(-n-z) 11

Suppose we have a periodic function f with period 2, defined on z € [-1, 1] by: The Fourier series of f is given by: NB: In this question you will need to simplify cos(n) and sin(n) by exploiting that n is an integer. In the Fourier series of f, what is the value of ag? In the Fourier series of f, what is the value of an for n € N? In the Fourier series of f, what is the value of the b for n € N? Check 0 -1 -2 -3 -4 -0.5 0 1 € (-1,0], T € (0, 1]. 0.5 F(x)= ao+an cos( n 1) + b₂ sin(-n-z) 11

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 71E
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Suppose we have a periodic function f with period 2, defined on z = [-1,1] by: The Fourier series of f is given by: NB: In this question you will need to simplify cos(n) and sin(n) by exploiting that is an integer. In the Fourier series of f, what is the value of an? In the Fourier series of f, what is the value of an for n E N? In the Fourier series of f, what is the value of the b, for n E N? Check 2 1 0 -1 -2 -3 -4 -1 f(x) = F(x) = a + -0.5 n=1 3 lz 0 I € [-1,0], T € (0, 1). 0.5 1 an cos(π nx) + b₂ sin(π · n · · ¹-x)
Transcribed Image Text:Suppose we have a periodic function f with period 2, defined on z = [-1,1] by: The Fourier series of f is given by: NB: In this question you will need to simplify cos(n) and sin(n) by exploiting that is an integer. In the Fourier series of f, what is the value of an? In the Fourier series of f, what is the value of an for n E N? In the Fourier series of f, what is the value of the b, for n E N? Check 2 1 0 -1 -2 -3 -4 -1 f(x) = F(x) = a + -0.5 n=1 3 lz 0 I € [-1,0], T € (0, 1). 0.5 1 an cos(π nx) + b₂ sin(π · n · · ¹-x)
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