10.15 Representing Functions as Power Series Calculus CA #1 Name: 1 . What is the coefficient of x'5 in the Taylor series for the function f (x) = ex sin x about x = 0? 2. If the function f is defined by f (x) =) n! , then f' (x) = ? Write the first four nonzero terms and the 1 = 0 general term of the Taylor series about x = 0. 3 . Let f be the function defined by f (x) = 3x. Find the Maclaurin series for the derivative f'. Write the first four nonzero terms and the general term.4 . Find the third-degree Taylor Polynomial for f (x) = sin x cos x about x = 0. 5. If f' (x) = = and f(0) = 0, write the first four nonzero terms and the general term of the Maclaurin series for f (x). Answers to 10.15 CA #1 N 3. 5