Approximate f (x) = x 2 on [0, ] with a linear combination
Chapter 6, Problem 6.93(choose chapter or problem)
Approximate f (x) = x 2 on [0, ] with a linear combination of the functions 1, cos(x), cos(2x), cos(3x), and cos(4x). Use p(x)=1 in the weighted inner product on this function space. Graph f (x) and the approximating linear combination on the same set of axes. Hint: Calculate fS , the orthogonal projection of f onto the subspace of C[0, ] spanned by 1, cos(x), , cos(4x).
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