Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 13 - Review - Exercises: 15

Answer

$\lim _{x\rightarrow 3 ^{-}}\dfrac {x-3}{\left| x-3\right| }=-1$

Work Step by Step

$x < a\Rightarrow \left| x-a\right| =a-x\Rightarrow \lim _{x\rightarrow 3 ^{-}}\left| x-3\right| =\left( 3-x\right) $ $\lim _{x\rightarrow 3 ^{-}}\dfrac {\left( x-3\right) }{\left| x-3\right| }=\dfrac {x-3}{3-x}=-1$
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