Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Mid-Chapter Check Point - Page 1163: 12


The value of $\underset{x\to -2}{\mathop{\lim }}\,\left( {{x}^{3}}-x+5 \right)$ is $-1$.

Work Step by Step

Consider the function $ f\left( x \right)={{x}^{3}}-x+5$, The function $ f\left( x \right)={{x}^{3}}-x+5$ is a polynomial. Find the value of $\underset{x\to -2}{\mathop{\lim }}\,\left( {{x}^{3}}-x+5 \right)$, $\begin{align} & \underset{x\to -2}{\mathop{\lim }}\,\left( {{x}^{3}}-x+5 \right)=\underset{x\to -2}{\mathop{\lim }}\,{{x}^{3}}-\underset{x\to -2}{\mathop{\lim }}\,x+5 \\ & ={{\left( -2 \right)}^{3}}-\left( -2 \right)+5 \\ & =-8+2+5 \\ & =-1 \end{align}$ Thus, the value of $\underset{x\to -2}{\mathop{\lim }}\,\left( {{x}^{3}}-x+5 \right)$ is $-1$
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