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 1138: 23

Answer

$\underset{x\to 2}{\mathop{\lim }}\,\left( 1-{{x}^{2}} \right)=-3$, since, as x approaches 2, the value of $ f\left( x \right)$ gets closer to the y-coordinate of $-3$.

Work Step by Step

Consider the provided limit $\underset{x\to 2}{\mathop{\lim }}\,\left( 1-{{x}^{2}} \right)$. To find $\underset{x\to 2}{\mathop{\lim }}\,\left( 1-{{x}^{2}} \right)$, examine the portion of the graph near $ x=2$. As x approaches 2, the value of $ f\left( x \right)$ gets closer to the y-coordinate of $-3$. This point $\left( 2,-3 \right)$ is shown by the solid dot in the above graph. The point $\left( 2,-3 \right)$ has a y-coordinate of $-3$. Thus, $\underset{x\to 2}{\mathop{\lim }}\,\left( 1-{{x}^{2}} \right)=-3$. Hence, the value of $\underset{x\to 2}{\mathop{\lim }}\,\left( 1-{{x}^{2}} \right)$ is $-3$.
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