Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 3 - The Derivative - 3.1 Limits - 3.1 Exercises - Page 137: 20


The limit does not exist.

Work Step by Step

Please see image attached for the values that need to be entered into the table. Reading the table, as $x$ approaches $3$ from the left, $f(x)$ seems to rise without bound, $\displaystyle \lim_{x\rightarrow 3^{-}}f(x)=+\infty$ as $x$ approaches $3$ from the right, $f(x)$ seems to descend without bound, $\displaystyle \lim_{x\rightarrow 3^{+}}f(x)=-\infty$ so we estimate that $\displaystyle \lim_{x\rightarrow 3}f(x)$ does not exist.
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