Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.4 Limits and Continuity - Exercises - Page 67: 53


$f(x)$ is neither left nor right continuous at $x=2$.

Work Step by Step

Given $$ f(x)=\left\{\begin{array}{ll} {\dfrac{x^{2}-3 x+2}{|x-2|}} & {x \neq 2} \\ {0} & {x=2} \end{array}\right. $$ From the figure, $$ \lim _{x \rightarrow 2^{-}} f(x) \neq \lim _{x \rightarrow 2^{-}} f(x) \neq f(2) $$ Then $f(x)$ is neither left nor right continuous at $x=2$ (there is a jump discontinuity at $x=2$).
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