MATH 1220 Midterm: CalcII_Midterm2_Summer2014
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Show all work and include appropriate explanations when necessary. Instructions. without accompanying work may not receive full credit. Please try to do all all work in the space provided and circle your nal answer: (20pts) evaluate the following limits using l"h opital"s rule or any other method. Note, the correct answer may be . (a) (5pts) lim x . 5x2 2x (b) (5pts) lim x 0+ cos x sin x x (c) (5pts) lim x . 2 cos x (d) (5pts) lim x 0 x2 cos x x sin x: (8pts) consider the sequence with rst ve terms given by a1 = 3 a2 = 1: (12pts) in this problem, we will compute the following improper integral in two steps. Note: this is an improper integral because the integrand x ln x is not continuous at x = 0. (a) (6pts) first compute z 1 t x ln x dx.
