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The Fourier series of a periodic function f(x) is given by 6+ cos(nz) + sin(nz). 6" n-1 The best approximation of f by a Fourier polynomial (or trigonometric polynomial) of degree 2 is 1 1) F(x) = cos z + 2 sinx+ cos(22) + sin(2r). 64 36 2) F(z) = 36 cos(2z) + sin(2z). 64 1 3) F(z) = 6+ 1 2 sin z + 36 cos(2z) -sin(2z). 6COS 64 1 4) F(x)= 6+ cos z +2 sin z+ 1 cos(2z) + sin(2x).

The Fourier series of a periodic function f(x) is given by 6+ cos(nz) + sin(nz). 6" n-1 The best approximation of f by a Fourier polynomial (or trigonometric polynomial) of degree 2 is 1 1) F(x) = cos z + 2 sinx+ cos(22) + sin(2r). 64 36 2) F(z) = 36 cos(2z) + sin(2z). 64 1 3) F(z) = 6+ 1 2 sin z + 36 cos(2z) -sin(2z). 6COS 64 1 4) F(x)= 6+ cos z +2 sin z+ 1 cos(2z) + sin(2x).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The Fourier series of a periodic function f(x) is given by 1 cos(nz) + 6+ sin(nz). 6 n=1 The best approximation of f by a Fourier polynomial (or trigonometric polynomial) of degree 2 is 1 cos z + 2 sin x+ 1 1) F(z) = cos(2a) + 36 sin(2r). 64 2) F(x)= cos(2r) + 36 sin(2a). 64 1 3) F(z) = 6+ cos z - 1 cos(2r) 2 sin a + sin(2z). 36 64 1 4) F(x) = 6+ cos a + 2 sin z+ 1 cos(2r) + 36 sin(2r). 64 1 5) F(r) = 6+ sin r + cos(2r) - sin(2a). COs a 36 64
Transcribed Image Text:The Fourier series of a periodic function f(x) is given by 1 cos(nz) + 6+ sin(nz). 6 n=1 The best approximation of f by a Fourier polynomial (or trigonometric polynomial) of degree 2 is 1 cos z + 2 sin x+ 1 1) F(z) = cos(2a) + 36 sin(2r). 64 2) F(x)= cos(2r) + 36 sin(2a). 64 1 3) F(z) = 6+ cos z - 1 cos(2r) 2 sin a + sin(2z). 36 64 1 4) F(x) = 6+ cos a + 2 sin z+ 1 cos(2r) + 36 sin(2r). 64 1 5) F(r) = 6+ sin r + cos(2r) - sin(2a). COs a 36 64
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