Let f(x) = {2 0 < x < π/2 π/2 < x
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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#4
Need parts A-G
![[4] Let
f(x) = {2
0 < x < π/2
π/2 < x < T.
(a) Sketch the even periodic extension of f.
(b) Find the Fourier cosine series of f.
(c) To what values does the Fourier cosine series converge at x = 0, x= x/2, x= x,x=
3π/2, and x = 2π?
(d) Sketch the odd periodic extension of f.
1
(e) Find the Fourier sine series of f.
(f) To what values does the Fourier sine series converge at x = 0, x = π/2, x = π, x =
3π/2, and x = 2π?
(g) Denote by fep(x) the even periodic extension of f(x).
When we use periodic functions of the form
T(x) = A + A₁ cos x + B₁ sin x + A₂ cos (2x) + B₂ sin(2x)
to approximate fep(x), the error in mean is defined by
fep(x) - T(x)|²dx.
-ग
Determine the values of coefficients A0, A1, B₁, A2, B2 that minimize the error in
mean.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa68164dd-6bba-4aa5-92bc-4824a71db092%2F9c71acc6-0afa-4ceb-a74f-8b36f8ab039f%2F9616zwl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[4] Let
f(x) = {2
0 < x < π/2
π/2 < x < T.
(a) Sketch the even periodic extension of f.
(b) Find the Fourier cosine series of f.
(c) To what values does the Fourier cosine series converge at x = 0, x= x/2, x= x,x=
3π/2, and x = 2π?
(d) Sketch the odd periodic extension of f.
1
(e) Find the Fourier sine series of f.
(f) To what values does the Fourier sine series converge at x = 0, x = π/2, x = π, x =
3π/2, and x = 2π?
(g) Denote by fep(x) the even periodic extension of f(x).
When we use periodic functions of the form
T(x) = A + A₁ cos x + B₁ sin x + A₂ cos (2x) + B₂ sin(2x)
to approximate fep(x), the error in mean is defined by
fep(x) - T(x)|²dx.
-ग
Determine the values of coefficients A0, A1, B₁, A2, B2 that minimize the error in
mean.
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