8. Recall that we can define an inner product on the set PC[a, b] as follows: (f.g) = ["f f(x)g(x) dx and we can define a norm on the same set as: ||f|| = √(f. f) a. Show that the functions f(x) = x and g(x) = cos (x) are orthogonal in the set PC[-π, π]. b. Compute the norm |cos (x) || in the set PC[-, π].

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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8. Recall that we can define an inner product on the set PC[a, b] as follows:
b
(f.g) = [" f(x) g(x) dx
and we can define a norm on the same set as:
||f|| = √(f, f)
a. Show that the functions f(x) = x and g(x) = cos (x) are orthogonal in the
set PC[-1, π].
b. Compute the norm ||cos (x) || in the set PC[-, π].
Transcribed Image Text:8. Recall that we can define an inner product on the set PC[a, b] as follows: b (f.g) = [" f(x) g(x) dx and we can define a norm on the same set as: ||f|| = √(f, f) a. Show that the functions f(x) = x and g(x) = cos (x) are orthogonal in the set PC[-1, π]. b. Compute the norm ||cos (x) || in the set PC[-, π].
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