Would a=pi here?

2. Consider the function f (9:) = 2: cos 3:. (a) Compute the 4th degree Taylor polynomial P403) about the point a: = 7?. (b) Find an upper bound on the error associated with P4($) on the interval 7r 5 a: 3 1r + 0.5. (e) Let In be an approximation to the integral I = [77+O.5 f($)d$, where f($) is approximated by Pn(L'). Find I4. (d) Using the upper bound obtained in (b), nd an upper bound on the error associated with the approximation I4 in part (0)