Find the trigonometric Fourier series for the function f(x): [-T/2, π/2] → R given by the expression: f(x) = { O cos 2x if x = [-π/2, 0] 0 if x = (0, π/2] FS(x) = -2 cos (2x) + En=1 FS(x) = cos(2x) + Σ-2 FS (x) = sin(2x) + Σn-2 FS(x) = cos(2x) + Σ FS(x) = cos(2x) + Ex-1 n² cos² (n²-1)π ² ( =) 2 2n cos² n cos² n cos² (n²-1) T 2(n²-1)T n=0 (n²-1) JLTT (+) 2 2n cos² 72T 2 (=) TLTT 2 -sin(2nx). (=) (n²+1) T -sin(2nx). -sin(nx). -sin(2nx). -sin(2nx).
Find the trigonometric Fourier series for the function f(x): [-T/2, π/2] → R given by the expression: f(x) = { O cos 2x if x = [-π/2, 0] 0 if x = (0, π/2] FS(x) = -2 cos (2x) + En=1 FS(x) = cos(2x) + Σ-2 FS (x) = sin(2x) + Σn-2 FS(x) = cos(2x) + Σ FS(x) = cos(2x) + Ex-1 n² cos² (n²-1)π ² ( =) 2 2n cos² n cos² n cos² (n²-1) T 2(n²-1)T n=0 (n²-1) JLTT (+) 2 2n cos² 72T 2 (=) TLTT 2 -sin(2nx). (=) (n²+1) T -sin(2nx). -sin(nx). -sin(2nx). -sin(2nx).
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
![Find the trigonometric Fourier series for the function f(x): [-T/2, π/2] → R given by the
expression:
ƒ(2) - {0
=
O
о
O
O
cos 2x if x = [-π/2, 0]
0 if x = (0, π/2]
O
∞
FS(x) = -2 cos(2x) + 1
n=1
FS(x) = −cos(2x) + Σ2
FS(x) = −sin(2x) + Σn=2
FS(x) = cos(2x) + Σn=0
FS(x) = cos(2x) + Ex-1
-
n² cos²
(n²-1)π
2n cos²
n cos²
(=)
2
n cos²
(n²-1)T
(+)
2
2(n²-1)π
NE
(+)
(n.²-1)
2n cos²
* ( =)
2
(n²+1)π
-sin(2nx).
-sin(2nx).
-sin(nx).
sin(2nx).
-sin(2nx).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7fe9d10e-89b5-480b-b9fb-b8733688f212%2Fea6d0c03-e137-4559-948b-c909763a8b59%2Fmwpklv9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find the trigonometric Fourier series for the function f(x): [-T/2, π/2] → R given by the
expression:
ƒ(2) - {0
=
O
о
O
O
cos 2x if x = [-π/2, 0]
0 if x = (0, π/2]
O
∞
FS(x) = -2 cos(2x) + 1
n=1
FS(x) = −cos(2x) + Σ2
FS(x) = −sin(2x) + Σn=2
FS(x) = cos(2x) + Σn=0
FS(x) = cos(2x) + Ex-1
-
n² cos²
(n²-1)π
2n cos²
n cos²
(=)
2
n cos²
(n²-1)T
(+)
2
2(n²-1)π
NE
(+)
(n.²-1)
2n cos²
* ( =)
2
(n²+1)π
-sin(2nx).
-sin(2nx).
-sin(nx).
sin(2nx).
-sin(2nx).
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