| Sots (X)dx=0, Seven (X)dx= 2√ Sv. (x)dx (c) By evaluating the first six Fourier coefficients show that the Fourier series of f(x) is given by: so 24 44(1
| Sots (X)dx=0, Seven (X)dx= 2√ Sv. (x)dx (c) By evaluating the first six Fourier coefficients show that the Fourier series of f(x) is given by: so 24 44(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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Question
please answer question C many thanks
![Question 2
Figure 1 shows a periodic function, f(x), with period of 2.
f(x)
–π ο π
0
n
Figure 1
X
24 1+(-1)"
π
1-n²
(a) State if the function f(x) has odd or even symmetry.
f(x)=
(b) Show that the Fourier coefficients of f(x) are given by:
A is a constant.
2A 4A
f(x)= 44 (= cos(2x) + cos(4
T
-24
Hint: You will find the result in question 1(b) useful to find an. Also, remember
that
| Loss (X)dx=0,_ ↑ Seven (X)dx=2] Som (x) dx
Asinx if 0≤x≤a
-Asinx if -≤x≤0
b₁ = 0
(c) By evaluating the first six Fourier coefficients show that the Fourier series of f(x)
is given by:
cos(4x) +
1
*35 cos(6x) +...](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F955e192e-949b-43db-b1bc-9e4d5aa0185f%2Fe7657bd9-6529-4b30-b6ee-22e3cfbb1419%2Far6v1hx_processed.png&w=3840&q=75)
Transcribed Image Text:Question 2
Figure 1 shows a periodic function, f(x), with period of 2.
f(x)
–π ο π
0
n
Figure 1
X
24 1+(-1)"
π
1-n²
(a) State if the function f(x) has odd or even symmetry.
f(x)=
(b) Show that the Fourier coefficients of f(x) are given by:
A is a constant.
2A 4A
f(x)= 44 (= cos(2x) + cos(4
T
-24
Hint: You will find the result in question 1(b) useful to find an. Also, remember
that
| Loss (X)dx=0,_ ↑ Seven (X)dx=2] Som (x) dx
Asinx if 0≤x≤a
-Asinx if -≤x≤0
b₁ = 0
(c) By evaluating the first six Fourier coefficients show that the Fourier series of f(x)
is given by:
cos(4x) +
1
*35 cos(6x) +...
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