MATH 201 Exam 1, Fall 2012

Math 201 Exam 1 (Fall 2012) H. Yamani - Please write your name and section number on your booklet - Please answer each problem on the indicated page(s) of the booklet. Any part of your answer that is not written on the indicated page(s) will not be graded. - Unjustified answers will receive little or no credit. Problem | (answer on pages 1 and 2 of the booklet). (7 points each) Which of the following sequences converge, and which diverge? Find the limit of each convergent sequence fe, =n) en 08 Fe) SVi,-— \n +In4 Problem 2 (answer on pages 3 and 4 of the booklet), (7 points cach) Which of the following series converge, and which diverge? Find the sum of the series when possible. S(O) oS att] n=1 iy 3A SOX, [er Problem 3 (answer on page 5 of the booklet). (22 points) Find the interval of convergence of the power series sf (1 UE (x -5)’ For what values of x does the series converge absolutely? Conditionally? Problem 4 (answer on page 6 of the booklet). AAi)(11 pts) Find the power series expansion for (x)= e* about the point x =0. Use the alternating “Ol series estimation theorem to approximate eta with an error of magnitude less than 107’. a ‘ s _fai) (11 pts) Find the power series expansion for g(x)=e* about the point x =0. Approximate ¢{0.5)by p,(0.5)and estimate the resulting error using Taylor’s Theorem.