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Consider the following function: -x – 2, -2 < x < -1 -1 < x < 1 1< x < 2. f(x) = { x, 2 - x, (i) Sketch the graph of f and find its Fourier series on [-2, 2]. (ii) Use the obtained series to deduce that: 1 1 Σ and > 8. (2k – 1)2 (2k – 1)4 96 - k=1

Consider the following function: -x – 2, -2 < x < -1 -1 < x < 1 1< x < 2. f(x) = { x, 2 - x, (i) Sketch the graph of f and find its Fourier series on [-2, 2]. (ii) Use the obtained series to deduce that: 1 1 Σ and > 8. (2k – 1)2 (2k – 1)4 96 - k=1

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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4. Consider the following function: -x – 2, -2 < x < -1 -1 < x < 1 1< x < 2. f(x) = x, 2 - x, (i) Sketch the graph of f and find its Fourier series on [-2, 2]. (ii) Use the obtained series to deduce that: 1 1 Σ (2k – 1)2 and 8 (2k – 1)4 96 | k=1 k=1
Transcribed Image Text:4. Consider the following function: -x – 2, -2 < x < -1 -1 < x < 1 1< x < 2. f(x) = x, 2 - x, (i) Sketch the graph of f and find its Fourier series on [-2, 2]. (ii) Use the obtained series to deduce that: 1 1 Σ (2k – 1)2 and 8 (2k – 1)4 96 | k=1 k=1
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