Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Section 2.4 - The Precise Definition of a Limit - 2.4 Exercises - Page 114: 16

Answer

$\lim\limits_{x \to 4} (2x-5)= 3$

Work Step by Step

Let $\epsilon \gt 0$ be given. Let $\delta = \frac{\epsilon}{2}$ Suppose that $\vert x-4 \vert \lt \delta$. Then: $\vert (2x-5)-3 \vert = \vert 2x-8 \vert = \vert 2(x-4) \vert = 2\vert x-4 \vert \lt 2\delta = 2(\frac{\epsilon}{2}) = \epsilon$ Therefore, $\lim\limits_{x \to 4} (2x-5)= 3$
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