MATH 121 Study Guide - Midterm Guide: Limit Of A Sequence, Absolute Convergence, Glassbridge Enterprises
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Instructions: the total time is 180 minutes, the total score is 150 points, show all your work. A correct answer without intermediate steps will receive no credit: if you need extra space for your solution, use the opposite sides of the pages. 4 sin x 3 cos x (10 points) You can use the answer from one part in your solution for another, if you need to. (5 4 = 20 points) (a) find the maclaurin series of the function f (x) = ln(cid:0) 1+x. 1 x(cid:1). (b) find the domain of convergence of the series you obtained in part (a). 4 (c) is the function f (x) = ln(cid:0) 1+x reasons for your answer. Give (d) for which value of n is lim x 0 x n ln(cid:18)1 + sin3(x2) 5: for each of the following series, determine whether it converges absolutely, converges conditionally or diverges.
