Answer
$-1$
Work Step by Step
With $x\to -4^-$, we have $x+4\lt0$ and $|x+4|=-x-4$. Thus
$$\lim_{x\to -4^-}\frac{|x+4|}{x+4}=\frac{\lim_{x\to -4^-}|x+4|}{\lim_{x\to -4^-}x+4}=\frac{-x-4}{x+4}=-1$$
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: 38
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