1. Let f(x) = (a) Find the Taylor series of f expanded at a: = 0 by substituting into the appropriate binomial series. Include up to the 6th order term in your expansion. (b) Use the Taylor series for f found in (a) to determine f(4)(0). (C) Use the Taylor series for f found in (a) to determine f(133)(0). [Hintz Look at the types of terms you see in your Taylor series] 2. Let g(2;) = eCS($)_1. (a) Determine the Taylor series for g expanded at as = 0 up the fourth degree term. (b) Use the series found in (a) to show that g has a local maximum or minimum at a: = 0. Classify it as a maximum or minimum. 2