Consider the function f(x) = cos(x). (a) Find the Taylor polynomials of P(x) centered at c = 0 for k = 0,1,2,3,4. (b) Use P3(x) to find an approximation of cos(0.4). (c) Using the error term from Taylor's theorem, find a lower bound and an upper bound for cos(0.4). (d) How does your answer compare to the value of cos(0.4) that your calculator gives?