S = {Po, P1, P2} , Po(r) = 1, Pi(1) = r, P2(r) = 5 (1 – 3r²) , is an orthogonal set. 1. Find the norms of po, Pi and p2- 2. Let f(x) = e². Find the following inner products on [–1, 1]: (Po, f), (P1,f), (P2, f), 3. Find the orthogonal projection of f onto the span of S. That is, (Pi, f). (Po, f), P:(x) llP Po(x) + (P1, f), (P2, f), Þ2(x) llP2 Pi (x) + Note: Notice that the term for i = 0, 1,2 is a real number and can be obtained from the first two questions. Therefore, the projection will be a second order polynomial. If you plot the projection and the function ƒ on [-1, 1] their graphs should be close to each other.

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