Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Section 11.1 - Finding Limits Using Tables and Graphs - Exercise Set - Page 1140: 54


$\lim_{x \to 0 }f(x)$ does not exist.

Work Step by Step

To find $\lim_{x\to 0 }f(x)$, examine the graph of $f$ near $x=0$. As $x$ gets closer to $0$ from the left, the values of $f(x)$ get closer to $0$. As $x$ gets closer to $0$ from the right, the values of $f(x)$ get closer to $1$. We conclude from the graph that $\lim_{x \to 0 }f(x)$ does not exist because the left- and right-hand limits are unequal.
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