C f ( n) (a ) The Taylor series of a smooth function f on [a, b] is f(x) = (x - a)". n! n=0 (a) Find the first 6 terms in the Taylor series of sina and cosa on [0, 2x] (b) Find the first 6 terms in the Taylor series of er on [0, 2x]. (c) Let i = v-1. Then ? = -1, 13 = -i, it = 1, etc. By substituting into your answer for (b), find the Taylor series for eir. (d) Using the Taylor series for cos x, sina and ed, prove that ell = cost + isinx This is called Euler's formula, one of the greatest of all time. (e) Hence show that elf = -1. This crazy formula relates the numbers 7, e, -1, and V-1