Answer
Does not exist
Work Step by Step
$\lim_{x\to 2^-}\frac{|x-2|}{x-2}=\lim_{x\to 2^-}\frac{-(x-2)}{x-2}=-1$
$\lim_{x\to 2^+}\frac{|x-2|}{x-2}=\lim_{x\to 2^+}\frac{x-2}{x-2}=1$
As the side limits are different, the limit does not exist.
Precalculus: Mathematics for Calculus, 7th Edition
by Stewart, James; Redlin, Lothar; Watson, Saleem
Published by
Brooks Cole
ISBN 10:
1305071751
ISBN 13:
978-1-30507-175-9
Chapter 13 - Section 13.2 - Finding Limits Algebraically - 13.2 Exercises - Page 913: 39
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