Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 10 - Section 10.1 - Limits: Numerical and Graphical Viewpoints - Exercises - Page 698: 4

Answer

does not exist

Work Step by Step

See table below. As x approaches the value 2 from the left, $f(x)$ becomes a very large in magnitude negative number. It does not approach any fixed value. As x approaches the value 2 from the right, $f(x)$ becomes a very large in magnitude positive number. It does not approach any fixed value. If $f(x)$ fails to approach a single fixed number as $x$ approaches $a$ from both sides, then we say that $f(x)$ has no limit as $x\rightarrow a$, or $\displaystyle \lim_{x\rightarrow a}f(x)$ does not exist. Thus, $\displaystyle \lim_{x\rightarrow 2}\frac{x^{2}-1}{x-2}$ does not exist.
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