Question: Question 3. For any two continuous functions f (x) and g(x), let the inner product (g) = [0 f(X)g(x)dx. (1) Find an orthogonal basis for

Question 3. For any two continuous functions f (x) and g(x), let the inner product (g) = [0 f(X)g(x)dx. (1) Find an orthogonal basis for the inner product space P = Span{1, 2x + 3x2} (2) Find the least squares approximation to the function f (x) = sin x by a quadratic function a + bx + car2 in the interval [0, 7:]. (You may need: I: sin(x)dx = 2; J; x sin(x)dx = 7:; E x2 sin(x)dx = 712 4; I: x3 sin(x)dx = 7r(7r2 6))

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