Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 13 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - Section 13.3 One-sided Limits; Continuous Functions - 13.3 Assess Your Understanding - Page 909: 25


The limit is $0$.

Work Step by Step

We see that as we move from the left and the right toward the $x$ value of $4$, the $y$ value tends toward $0$. Since the left and right limits agree, the overall limit exists and is equal to $0$. This is true even though $f(4)$ does not exist (hole at $x=4$).
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