Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.2 Limits: A Numerical and Graphical Approach - Exercises - Page 54: 12


See the proof below.

Work Step by Step

We have $$ |7x-4-10| = |7x-14| =7|x-2|.$$ Since $|7x-4 − 10| $ is a multiple of $|x-2|$, then $|7x-4 − 10| $ is small whenever $ x $ is close to $2$. Hence, we get $$ \lim_{x\rightarrow 2}7x-4=10.$$
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