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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer the question with steps… Thank You
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe495063f-653c-4a5a-aab6-0ac14b7f3dc2%2F5c4f1738-4683-40c9-88ec-c1abb3445f97%2Fy12sz7_processed.jpeg&w=3840&q=75)
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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