4. (20 points) Define f(x) = x -2≤ x < −1, −1 ≤ x ≤ 1, x -1 1≤ x ≤2, and let f be periodic on (-∞, ∞0) with period 4. (a) (10 points) Sketch the graph of ƒ for −6 ≤ x < 6. (b) (10 points) Find the formula for the Fourier series S(f) on [-2,2) using the Fourier convergence theorem.
4. (20 points) Define f(x) = x -2≤ x < −1, −1 ≤ x ≤ 1, x -1 1≤ x ≤2, and let f be periodic on (-∞, ∞0) with period 4. (a) (10 points) Sketch the graph of ƒ for −6 ≤ x < 6. (b) (10 points) Find the formula for the Fourier series S(f) on [-2,2) using the Fourier convergence theorem.
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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Transcribed Image Text:4. (20 points) Define
f(x) =
x
-2≤ x < −1,
−1 ≤ x ≤ 1,
x -1 1≤ x ≤2,
and let f be periodic on (-∞, ∞0) with period 4.
(a) (10 points) Sketch the graph of ƒ for −6 ≤ x < 6.
(b) (10 points) Find the formula for the Fourier series S(f) on [-2,2) using the
Fourier convergence theorem.
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