Exercise 1: The function (f), periodic, is defined by: f(x) = x? si xe[- 7;1] The Fourier series of the function (f) is as follows: n=+00 Σ f(x) 3D аo - an cos(nx). n=1 1. What is the period of this function? 2. Give the graphical representation of the function (f) for xe[0: 3r]. 3. Determine ao et an.
Exercise 1: The function (f), periodic, is defined by: f(x) = x? si xe[- 7;1] The Fourier series of the function (f) is as follows: n=+00 Σ f(x) 3D аo - an cos(nx). n=1 1. What is the period of this function? 2. Give the graphical representation of the function (f) for xe[0: 3r]. 3. Determine ao et an.
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 find attached picture can you please let me know if you can answer the question
![Duration: 12 hours
Exercise 1 :
The function (f), periodic, is defined by:
f(x) 3 х? si xе[-п; т]
The Fourier series of the function (f) is as follows:
n=+00
f(x) — а, +
an cos(nx).
n=1
1.
What is the period of this function?
2.
Give the graphical representation of the function (f) for xe[0; 31].
3.
Determine ao et an-
Deduct the sum: Sn=+0(-1)“
n2
2n=1
5.
Using Parseval's formula
n=+00
1
1
| [f(x)]? dx =
af +
a + bỉ ,
n=1
To show that : yn=+0-
n4
Zn=1
90
||
4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40324ad2-76ec-40f8-9ce6-bd770ddaf3da%2F56b52de2-1777-4ed7-8ab3-cd78bf1dc852%2Fs7ns_processed.png&w=3840&q=75)
Transcribed Image Text:Duration: 12 hours
Exercise 1 :
The function (f), periodic, is defined by:
f(x) 3 х? si xе[-п; т]
The Fourier series of the function (f) is as follows:
n=+00
f(x) — а, +
an cos(nx).
n=1
1.
What is the period of this function?
2.
Give the graphical representation of the function (f) for xe[0; 31].
3.
Determine ao et an-
Deduct the sum: Sn=+0(-1)“
n2
2n=1
5.
Using Parseval's formula
n=+00
1
1
| [f(x)]? dx =
af +
a + bỉ ,
n=1
To show that : yn=+0-
n4
Zn=1
90
||
4.
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