1. (10 points) Let HI) = ln(1 + 33:] for all it E [(1. b]. (a) Determine the nth degree Taylor polynomial of f centered at a. Remember to check rst if the function satises the assumptions of Taylor's Formula. (1)] Compute the secondorder Taylor polynomial of f at the point a = 2. 2. (10 points) Consider the power series f(3:) = Z 4 (a) Find the interval and radius of convergence of x]. (1)] Find f'(:i:) and determine its interval of convergence. 3. (7 points each) Find the Maclaurin series expansion of the following functions and nd the radius of convergence. (a) x] = 12 sin (i) 71' 1 (5 + as)? e (b) ?) = (Hint: Use the Binomial series expansion.) (:2) H112) = "Eds