Math 1132 Exam 2 Part 2: Short Answer Problem 10: Determine if the following series converge or diverge by applying an appre priate convergence test. Be sure to check all conditions of the test that you are applying [A] ) n' + An nel Vn + 2n + 1 L n 50 n=1 00 [C] 2 2n3 + 4 n=1 [D] ( n ! ) 2 n = 0 ( 2n ) ! 00 [E] _ ne-n2 n= 1 Problem 11: Find the interval and radius of convergence of the following power series: [A] (-1) n2 (x - 3)n In 2 n= 1 [B] In! (x+ 10 ) n n= 1 Vn Problem 12: Determine if the following series is absolutely convergent, conditionally con- vergent, or divergent. You must show all of your work and indicate the tests that you are using: ( - 1 ) nn n= 1 Vn3 + 2 Page 4 of 6Math 1132 Problem 13: Consider the series: Exam 2 n = 1 n + 3 [i] Find an expression for the Nth partial sum SN of this series. [ii] Use SN to determine if the series converges or diverges. If it converges, find the sum. Problem 14: Determine the sum of the following geometric series: 3 - 6 12 24 15 25 125 + ... Problem 15: Find the specified Taylor polynomial TN(x) for each of the following functions centered at the indicated point. [A] T2(x) for f(x) = 12/3 at x = 8 [B] To(x) for f(x) = sin(2x) at I = Problem 16: Find a MacLaurin Series for each of the following functions: [A] f(x) = cos(21?) [B] f(x) = 24(ex? - 1) 1 [C] f(x) = (3x + 1)? Page 5 of 6F6 FZ Math 1132 Exam 2 Problem 17: Let's approximate cos (x2 ) dx. [A] Find the MacLaurin series for the indefinite integral / cos (x2) dx [B] Using your series from [A], find the first three terms of a series representation of the 1/5 definite integral cos (x2) dx. You do not need to simplify any expressions. [C] If we use the three terms from [B] to approximate cos (x2 ) dx, use the Alternating Series Remainder Estimate to give a bound on the error in our approximation. You do not need to simplify any expressions. Page 6 of 6