Question: Let V be the vector space V = {f : [0, 1] R : f is continuous} of continuous functions from [0, 1] to R.

Let V be the vector space V = {f : [0, 1] R : f is continuous} of continuous functions from [0, 1] to R. Give it the inner product f, g = 1 0 f (x)g(x) dx. (a) What is the orthogonal projection projx(sin 2x) of sin 2x on x? (b) What is the orthogonal projection projcos 2x(sin 2x) of sin 2x on cos 2x

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