Question: 3. Let f : [0, 1] - R be defined as f(x) = r = 1 for any n E N, sin(x), x / 1.

3. Let f : [0, 1] - R be defined as f(x) = r = 1 for any n E N, sin(x), x / 1. (a) Show that for any e > 0, there exists a continuous function g defined on 0, 1] such that If(x) - g(x) dx 0, there exists a polynomial h such that If (x) - h(x)|2 dx

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