Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 2 - Limits - 2.2 Definitions of Limits - 2.2 Exercises - Page 66: 16

Answer

a) 2; b) 0;

Work Step by Step

We are given the function: $g(x)=\dfrac{e^{2x}-2x-1}{x^2}$ a) Graph $g$ to estimate $\lim\limits_{x \to 0} g(x)$: From the graph we find: $\lim\limits_{x \to 0} g(x)=2$ b) Evaluate $g(x)$ for values near 0: $g(-0.1)\approx 1.87331$ $g(-0.01)\approx 1.98673$ $g(-0.001)\approx 1.99867$ $g(0.001)\approx 2.001334$ $g(0.01)\approx 2.013400$ $g(0.1)\approx 2.140276$ The values we found prove that the conjecture from part $a)$ is true: $\lim\limits_{x \to 0} g(x)=2$
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