Exam 1 with Answers - Calculus and Analytic Geometry | MATH 221, Exams of Analytical Geometry and Calculus

Download Exam 1 with Answers - Calculus and Analytic Geometry | MATH 221 and more Exams Analytical Geometry and Calculus in PDF only on Docsity! Exam 1 A. Miller Fall 97 Math 221 Show all work. 5 points per problem. 1. Sketch the graph of the function g(x) =  1− x if x ≤ −1 x + 3 if −1 < x < 2 2x− 1 if 2 ≤ x Use the graph to state the value of each of the following limits, if it exists. (a) limx→−1− g(x) (b) limx→−1+ g(x) (c) limx→0 g(x) (d) limx→2− g(x) (e) limx→2+ g(x) 2. Evaluate the limit, if it exists. limx→2 x4−16 x−2 . 3. State the definition of f(x) is continuous at a. Use the definition of con- tinuous and the properties of the limit to show that f(x) = 1 x+3 is continuous at x = 1. 4. Find the horizontal and vertical asymptotes of the curve y = 2x3 − x2 + 4x 27− x3 5. Find the equation of the tangent line to the curve y = x 2− x at the point (0, 0).