1. Consider the function f(x Z z which is defined by a power series. = Vn a. Use the Ratio Test to find the radius of convergence of the power series, then determine the interval of convergence. Show all relevant steps, including the tests required for the endpoints. (6 points) b. Determine the power series for f'(x) and its interval of convergence. Show all relevant steps. (3 points) . Determine the power series for f f(x)dx . You do not need to determine its interval of convergence. (1 point) \f". Radius of Convergence n+ 2 bn nt 1 : 3 = him = lim n-700 3 . Vht2 = 3 lim = 3 nt 2 Therefore , we need to Check the convergence at a = 7 +3 = 10 X = 7 - 3= 4at x= 10, The series Is h ( 10 - 7) 1 - 1 3h = 3 3 This is divergent series as noth term tends to infinity when n-70.Similarly for 2=4 , The Series n ( - 3 ) 7 - 1 3 n = ( - in ! In 3 Again, by alternating Series test , Since nifl 3 3 The series is divergent\f