6. The function g has derivatives of all orders for all real numbers. The Maclaurin series for g is given by 8(x) = S (-1)" x 2e" + 3 - on its interval of convergence. (a) State the conditions necessary to use the integral test to determine convergence of the series iM 8 7=0eh Use the integral test to show that iM 8 converges. n=0 (b) Use the limit comparison test with the series I M 8 n to show that the series g(1) = - (-1)" n=02e"+ 3 converges absolutely. (c) Determine the radius of convergence of the Maclaurin series for g. (d) The first two terms of the series g(1) = > (- 1) " n=0 2e" + 3 are used to approximate g(1). Use the alternating series error bound to determine an upper bound on the error of the approximation