Spring 2021 #5. Let po(x) = 1 and p(x) = x, and let P be the...

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Spring 2021 #5. Let po(x) = 1 and p₁(x) = x, and let P₁ be the subspace of the space C([0, 2]) of all continuous functions on [0, 2] spanned by po and p₁- (a) Find a basis for P₁ which is orthonormal with respect to the inner product (f. g) = f f(t)g(t) dt. (b) Use the results of Part (a) to find the function f(x) = ax + b in P₁ which makes the quantity J(f) = √²/2² - f(x)² dx as small as possible. Spring 2021 #5. Let po(x) = 1 and p₁(x) = x, and let P₁ be the subspace of the space C([0, 2]) of all continuous functions on [0, 2] spanned by po and p₁- (a) Find a basis for P₁ which is orthonormal with respect to the inner product (f. g) = f f(t)g(t) dt. (b) Use the results of Part (a) to find the function f(x) = ax + b in P₁ which makes the quantity J(f) = √²/2² - f(x)² dx as small as possible.

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Som given let Px 1 and P x x and let P be the Space c 02 of all continuous by Po ... View the full answer