Problem 6 (15 marks) In this problem we are going to approximate the function f(x) = cos(x) about x =0 using a simple function of the form 8 (x) 1 +a.x 1 + b. x2 The goal will be to find the best parameters a and b. (a) [5 marks] Find the Taylor series of _ about x = 0. (b) [5 marks] Use your answer to part (a) to find the first three non-zero terms of the Taylor series for g(x) about x = 0. (c) [5 marks] Find the parameters a and b which guarantee that your answer to part (b) agrees with the first three non-zero terms in the Taylor series for f(x) = cos(x) about x = 0