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 - Preliminary Questions - Page 66: 3



Work Step by Step

$\lim\limits_{x \to 0^{-}}f(x)\gt 1$ $\lim\limits_{x \to 0^{+}}f(x)\lt 0$ $\implies \lim\limits_{x \to 0^{-}}f(x)\ne\lim\limits_{x \to 0^{+}}f(x)$ One of the conditions for the function to be continuous at 0 is the existence of the limit at 0. As the left-hand limit and right-hand limit doesn't coincide, $\lim\limits_{x \to 0}f(x)$ doesn't exist. Therefore, the function $f$ can't be continuous.
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