5. In this exercise we investigation the Taylor series of polynomial functions. a. Find the 3rd order Taylor polynomial centered at a = = 0 for f(x) = x- 2x + 3x - 1. Does your answer surprise you? Explain. b. Without doing any additional computation, find the 4th, 12th, and 100th order Taylor polynomials (centered at a = 0) for f(x) = x- 2x + 3x - 1. Why should you expect this? c. Now suppose f(x) is a degree m polynomial. Completely describe the nth order Taylor polynomial (centered at a = 0) for each n.