MATH 1100Y Quiz: MATH1100Y-Quizzes
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Mathematics 1100y calculus i: calculus of one variable. Let f (x) = 2x 1: sketch the graph of f (x). [2: sketch the graph of f 1(x), the inverse function of f (x). [1: find a formula for f 1(x). Consider the parametric curve given by y = cos(2t) and x = cos(t), where . 2: show that every point on this curve is on the parabola given by y = 2x2 1. [3: sketch the parametric curve. (warning: it is not all of the parabola . [10 minutes: compute lim x 0 (x + 1) sin(x) x2 + x. Do one (1) of questions 1 or 2: compute lim x x2 + cos(x) [5: let f (x) = 3x + 2. Use the limit de nition of the derivative to show that f (x) = 3. [10 minutes: compute f (x) for f (x) = arctan(cid:18) x x + 1(cid:19).
