MATH 1220 Midterm: CalcII_Midterm2_Summer2013
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Show all work and include appropriate explanations when necessary. Instructions. without accompanying work may not receive full credit. Hint: rewrite as a fraction of indeterminate type (d) (4pts) lim x 0 sin x x x3: (8pts) consider the sequence with rst ve terms given by a1 = 1 a2 = 1: (11pts) in this problem, you will compute the value of an improper integral in two steps. (a) (7pts) use integration by parts to compute the de nite integral. Note: your answer should be a function of t. 0 xe x dx. (b) (4pts) take the limit as t of your answer in part (a) to nd. 0 xe x dx: (15pts) all of the following series are convergent. 2: (20pts) determine, by whatever method you wish, whether the following series are convergent or divergent. Circle c" if the series is convergent or d" if the series is divergent. N4 + 1 ( 1)n ln n n2 n!
