(30 points) Let V be the space of [-1,1] →→ R continuous functions, and define (ƒ,g) = f'¹₁ f(t)g(t)dt. Let W be the sub

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30 Points Let V Be The Space Of 1 1 R Continuous Functions And Define F G F F T G T Dt Let W Be The Sub 1 (91.52 KiB) Viewed 35 times

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(30 points) Let V be the space of [-1,1] →→ R continuous functions, and define (ƒ,g) = f'¹₁ f(t)g(t)dt. Let W be the subspace of [-1, 1] →→R polynomial functions with degree no greater than 2. 1 (a) (10 points) Show that (ƒ, g) defined above is an inner product. (b) (15 points) Consider ß = {1, x, x²} as a basis of W. Based on ß, use the Gram-Schmidt process to find an orthonormal basis of W. (c) (5 points) Compute the "best" (closest) second-degree polynomial approximation of the function h(t) = e¹ on [-1, 1].