4(a) A function f(x) defined on [0, 1] may be represented by its Fourier cosine series given by 1 2 f f(x) cos(n7x) dx, n ≥ 0. ao %+E 2 n=1 + Σan cos(nπχ), where an = 2 Use this formula to find the an, n ≥ 0, for the Fourier cosine series of the function f(x) = {0 0 ≤ x ≤ 1, < x≤ 1. 4 As sin(n) = 0 for any integer n, your expressions for the an should not contain any sin(nл) terms. (b) For the Fourier cosine series found in part (a), what are its values at x = 1/4, x = 0, and = −1/4? X =
4(a) A function f(x) defined on [0, 1] may be represented by its Fourier cosine series given by 1 2 f f(x) cos(n7x) dx, n ≥ 0. ao %+E 2 n=1 + Σan cos(nπχ), where an = 2 Use this formula to find the an, n ≥ 0, for the Fourier cosine series of the function f(x) = {0 0 ≤ x ≤ 1, < x≤ 1. 4 As sin(n) = 0 for any integer n, your expressions for the an should not contain any sin(nл) terms. (b) For the Fourier cosine series found in part (a), what are its values at x = 1/4, x = 0, and = −1/4? 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(a) A function f(x) defined on [0, 1] may be represented by its Fourier cosine series given by
ao
№
∞
+ Σ an cos(nπχ),
n=1
where
Аs sin(n)
sin(nл) terms.
1
: ²2²
[ f(x) cos(nxx) dx, n ≥ 0.
an = 2
Use this formula to find the an, n ≥ 0, for the Fourier cosine series of the function
X
f(x) = {0,₂ 0 ≤ x ≤ 1,
1,
1<x<1.
4
=
0 for any integer n, your expressions for the an should not contain any
(b) For the Fourier cosine series found in part (a), what are its values at x = 1/4, x = 0, and
x = -1/4?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc7689b9-c4fe-4bee-b670-05d15f3915cb%2F0a2bc648-250d-4308-95a2-b2897fc546eb%2F2ho1m5e_processed.png&w=3840&q=75)
Transcribed Image Text:4(a) A function f(x) defined on [0, 1] may be represented by its Fourier cosine series given by
ao
№
∞
+ Σ an cos(nπχ),
n=1
where
Аs sin(n)
sin(nл) terms.
1
: ²2²
[ f(x) cos(nxx) dx, n ≥ 0.
an = 2
Use this formula to find the an, n ≥ 0, for the Fourier cosine series of the function
X
f(x) = {0,₂ 0 ≤ x ≤ 1,
1,
1<x<1.
4
=
0 for any integer n, your expressions for the an should not contain any
(b) For the Fourier cosine series found in part (a), what are its values at x = 1/4, x = 0, and
x = -1/4?
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