Use the inner product〈f,g〉=∫10f(x)g(x)dxin the vector space C0[0,1] of continuous functions on the domain [0,1] to find 〈f,g〉, ∥
f∥, ∥g∥, and the angle αf,g between f(x) and g(x) forf(x)=−10x2−6 and g(x)=−9x−4.〈f,g〉= ,∥f∥= ,∥g∥= ,αf,g .
1 answer:
Answer:
a) <f,g> = 2605/3
b) ∥f∥ = 960
c) ∥g∥ = 790
d) α = 90
Explanation
a) We calculate <f,g> using the definition of the inner product:
b) How
∥f∥ = <f,f> then:
∥f∥ =
c)
∥g∥ = <g,g>
∥g∥ =
d) Angle between f and g
<f,g> = ∥f∥∥g∥cosα
Thus
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