Show that the given set of functions is orthogonal on the indicated interval. Find the norm of each function in the set. {1, cos(x)}, n = n = 1, 2, 3, ... ; [0, p] For m # n P m) Lº cos(x) cos((2x) dx = 21" (ccs( 19 - 04x) + ( cos( COS . || = 0 1 H|2 sin((n - m)n)x P (n-m)n P (n + m) n P -X (sin((n + m)))x P (n + m)π P )) dx ) X
Show that the given set of functions is orthogonal on the indicated interval. Find the norm of each function in the set. {1, cos(x)}, n = n = 1, 2, 3, ... ; [0, p] For m # n P m) Lº cos(x) cos((2x) dx = 21" (ccs( 19 - 04x) + ( cos( COS . || = 0 1 H|2 sin((n - m)n)x P (n-m)n P (n + m) n P -X (sin((n + m)))x P (n + m)π P )) dx ) 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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Question
![Show that the given set of functions is orthogonal on the indicated interval. Find the norm of each function in the set.
{1, cos(x)}, n =
For m # n
n = 1, 2, 3, ...; [0, p]
P
-
COS
dx =
L ²00 (² x ) 20 (1 x) Cx - + [² ( c²²( 10 = ² x) = (cos((n + m) x.
+ COS
-X
2
р
||
=
0
1
2
sin((n - m)n)x
P
(n-m)n
P
(sin((n + m)))x
P
(n + m)π
P
)) dx
)
Xx](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd8d776ae-c221-44f7-bbf2-f74f003dec75%2F594b5d17-8c65-4b4d-97f6-7f4423844265%2Fvn0tr1j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Show that the given set of functions is orthogonal on the indicated interval. Find the norm of each function in the set.
{1, cos(x)}, n =
For m # n
n = 1, 2, 3, ...; [0, p]
P
-
COS
dx =
L ²00 (² x ) 20 (1 x) Cx - + [² ( c²²( 10 = ² x) = (cos((n + m) x.
+ COS
-X
2
р
||
=
0
1
2
sin((n - m)n)x
P
(n-m)n
P
(sin((n + m)))x
P
(n + m)π
P
)) dx
)
Xx
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