using sage. p is F,g

2. (25 points) Let CR(-7, 7] denote the real inner product space of contin- uous real-valued functions on (-7, 7) with inner product 70 (5,9) = { $(6)g(t) dt. - (a) Let P be defined as above. Find an orthonormal basis for P. (b) Find a polynomial u(t) that best approximates f(t) = sin(t)e'. (c) Compare the graphs of ult) and f(t). 2. (25 points) Let CR(-7, 7] denote the real inner product space of contin- uous real-valued functions on (-7, 7) with inner product 70 (5,9) = { $(6)g(t) dt. - (a) Let P be defined as above. Find an orthonormal basis for P. (b) Find a polynomial u(t) that best approximates f(t) = sin(t)e'. (c) Compare the graphs of ult) and f(t)