⟨f,g⟩=∫10f(x)g(x)dx in 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) for f(x)=−10x2−9 and g(x)=9x+3

Answer 1

This is straight forward. For example, for the <f(x),g(x)> just evaluate the integral from 0 to 1 of the function 10(-10x^{2}-9)(9x+3). Similarly for the remaining expressions.