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: 9


See the proof below.

Work Step by Step

We have $$ |3 x-12|=3|x-4| $$ Since $|3x-12| $ is a multiple of $|x-4|$, then we see that $|3x-12| $ is small by taking $ x $ sufficiently close to $4 $. Hence, we have $$ \lim _{x \rightarrow 4} 3x=12.$$
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