Chemistry 27 Midterm: CHEM27 Harvard 2006ExamIChem27answers
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Write all answers (a, b, c, d, e, f) in the spaces provided below! 1: determine if the series is convergent or divergent. 2: how many of the following series converge. X n=1 n2 + 3 (n + 4)2. 3: which statement is true of the following series (ia) D. ) both the rst and second series converge. E. ) both the rst and third series converge. F. ) both the second and third series converge. 5: a curve is de ned by the parametric equation x = t t3, y = 3t2. Notice that the curve goes through the point (0, 3) for two distinct values of t and hence has a loop. 7: consider the cartesian coordinate (x, y) = (2 3, 2). Find the polar coordinate (r, ) where r > 0, and 0 < 2 . 8: find the limit of the sequence {n tan( 1. 9: de ne a sequence a1 = 2, a2 = 21+ 1.
