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 13.1 Finding Limits Using Tables and Graphs - 13.1 Assess Your Understanding - Page 896: 21

Answer

The limit does not exist.

Work Step by Step

As we can see as $x$ gets closer and closer to $3$ from the left, the value of the function (the y-value) gets closer and closer to $3$. But, as we can see as $x$ gets closer and closer to $3$ from the right, the value of the function (the y-value) gets closer and closer to $6$. Thus the limits from the two sides differ, thus the limit does not exist.
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