Chemistry 27 Midterm: CHEM27 Harvard 2006ExamIChem27Questions
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Write all answers (a, b, c, d, e, f) in the spaces provided below! 1: determine whether the sequence converges or diverges. 2: how many of the following series converge. 3: which statement is true of the following series (i) 5: a curve is de ned by the parametric equation x = t3 4t, y = 2 3(t2 4). This curve goes through the origin twice and hence has a loop. 6: find the equation for the line tangent to the curve de ned by the parametric equation x = et, y = sin(3t) at the point (x, y) = (1, 0) 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 cos( 1. 9: de ne a sequence a1 = 3, a2 = 31+ 2.
