Given the vector space C[1, 1] with inner product f , g = 1 1 f(x)g(x) dx and norm f =
Chapter 5, Problem 29(choose chapter or problem)
Given the vector space C[1, 1] with inner product f , g = 1 1 f(x)g(x) dx and norm f = (f , f) 1/2 (a) Show that the vectors 1 and x are orthogonal. (b) Compute 1 and x. (c) Find the best least squares approximation to x1/3 on [1, 1] by a linear function l(x) = c11 + c2x. (d) Sketch the graphs of x1/3 and l(x) on [1, 1]. 30. Co
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