11. Find the power series representation for g centered at 0 by differentiating or integrating the power series for f (perhaps more than once). Give the interval of convergence for the resulting series. X g(x)= using f(x)= (1+22)2 1 1+2x2 g(x) = k=0 The power series g(x) converges on the interval (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) 15. Find the function represented by the following series and find the interval of convergence of the series. k=0 (x-3)2k 4k The function represented by the series (x-3)2k is f(x) = 4k k=0 The interval of convergence is (Simplify your answer. Type your answer in interval notation.)