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MATH 1100Y Quiz: MATH1100Y-Quizzes (3)

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turquoisegnu128

31 Jan 2019

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Trent University

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Mathematics 1100y calculus i: calculus of one variable. [10 minutes: suppose the graph of y = x2 is stretched vertically by a factor of 3, and then shifted by 2 units to the right and 1 unit down. Find the formula of the parabola with this curve as its graph. [5: use the limit laws to evaluate lim x 0 x2 1 x2 + 1. Do one (1) of the following two questions: find all the vertical and horizontal asymptotes of f (x) = and give a rough sketch of its graph. [10: use the de nition of limits to verify that lim x 1. [10 minutes: compute the derivative of f (x) = [5: compute the derivative of g(x) = arctan (ex). [5] x2 2x x 1 x x 1 (3x 1) = 2. [12 minutes: use logarithmic di erentiation to compute the derivative of g(x) = xx.

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