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: 15

Answer

a) 0; b) 0;

Work Step by Step

We are given the function: $f(x)=\dfrac{x-2}{\ln |x-2|}$ a) Graph $f$ to estimate $\lim\limits_{x \to 2} f(x)$: From the graph we find: $\lim\limits_{x \to 2} f(x)=0$ b) Evaluate $f(x)$ for values near 2: $f(1.9)\approx 0.04343$ $f(1.99)\approx 0.00217$ $f(1.999)\approx 0.000145$ $f(2.001)\approx -0.000148$ $f(2.01)\approx -0.00217$ $f(2.1)\approx -0.0434$ The values we found prove that the conjecture from part $a)$ is true: $\lim\limits_{x \to 2} f(x)=0$
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