Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.4 Exercises: 106

Answer

False.

Work Step by Step

$\lim\limits_{x\to1^-}f(x)=\lim\limits_{x\to1^-}\dfrac{|x-1|}{x-1}=\dfrac{|1^--1|}{1^--1}=\dfrac{0^+}{0^-}=-1.$ $\lim\limits_{x\to1^+}f(x)=\lim\limits_{x\to1^+}\dfrac{|x-1|}{x-1}=\dfrac{|1^+-1|}{1^+-1}=\dfrac{0^+}{0^+}=1.$ Since $\lim\limits_{x\to1^+}f(x)\ne\lim\limits_{x\to1^-}f(c),$ then $\lim\limits_{x\to1}f(x)$ does not exist and the function has a discontinuity at $x=1.$ The function is continuous over the interval $(-\infty, 1)$ U $(1, \infty).$
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