## Calculus (3rd Edition)

Published by W. H. Freeman

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

#### Answer

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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