The exam has 10 problems for a total of 100 possible points. You must show all work, but you need not simplify your answers unless instructed to do so. Determine if the following series converges or diverges. X n=1 n + 20 pn5 + n2 + 15/n. Determine if the following series converges absolutely, converges conditionally, or diverges. One of the following series converges and one diverges. Indicate your method, and give reasons for your answer. X n=1 n + 1 n3en (x 2)n. (a) determine the center of the power series. (b) determine the radius of convergence for the power series. (c) determine the interval of convergence for the power series. Let f (x) = cos(x). (a) compute the taylor polynomial p2(x) of order 2 at a = 0 for f . (b) evaluate p2( /2). (c) taylor"s theorem states that.
