1. (8 points) In this problem, you will approximate In(1.2) using the Taylor series of In x centered at 1. (a) Find the first four derivatives of f(x) = In x and evaluate each one at the given center; that is c = 1. Then find the first five coefficients ak = f) (1) k! , where k = 0, 1, 2, 3, 4. Please use the following table to organize your answers. f ( k) ( 2) f( k) (1) ak = f ( k) (1 ) k! f (ac) = In ac f' (ac) = f"(ac ) = f (3) ( 20 ) = f ( 4 ) ( 20 ) = (b) Find the Taylor series of In(x) centered at 1. Write your answer in both sigma and . . . notation (with at least three terms written out). (c) Assume that the Taylor series of In(x) centered at 1 converges to In(x) for 0