Question

8. Recall that we can define an inner product on the set PC[a, b] as follows: $$(f,g) = \int_a^b f(x)g(x)dx$$ , and we can define a norm on the same set as: $$||f|| = \sqrt{(f,f)}$$ 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,π].

Name: 8 recall that we can define an inner product on the set pca b as follows fg intab fxgxdx and we can define a norm on the same set as f sqrtff a show that the functions fx x and gx cos x are 39741
Uploaded: 2022-02-08T14:36:49-08:00
Duration: 2 min 6 s
Channel: Ahmad Reda
Description: 8 recall that we can define an inner product on the set pca b as follows fg intab fxgxdx and we can define a norm on the same set as f sqrtff a show that the functions fx x and gx cos x are 39741

          8. Recall that we can define an inner product on the set PC[a, b] as follows:
$$(f,g) = \int_a^b f(x)g(x)dx$$
, and we can define a norm on the same set as:
$$||f|| = \sqrt{(f,f)}$$
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,π].

8 recall that we can define an inner product on the set pca b as follows fg intab fxgxdx and we can define a norm on the same set as f sqrtff a show that the functions fx x and gx cos x are 39741

Added by Daniel K.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ahmad Reda

02/08/2022

Step 1

The inner product is defined as: $$(f, g) = \int_{-\pi}^{\pi} x \cos(x) dx$$ Show more…

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8. Recall that we can define an inner product on the set PC[a, b] as follows: $$(f,g) = \int_a^b f(x)g(x)dx$$ , and we can define a norm on the same set as: $$||f|| = \sqrt{(f,f)}$$ 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,π].