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 1139: 37

Answer

$\underset{x\to -1}{\mathop{\lim }}\,\left| x+1 \right|=0$, because as x approaches $-1$, the value of $ f\left( x \right)$ gets closer to 0.
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Work Step by Step

Consider the provided function, $ f\left( x \right)=\left| x+1 \right|$. To plot the graph of the function $ f\left( x \right)=\left| x+1 \right|$ substitute different values of x in the equation $ f\left( x \right)=\left| x+1 \right|$ to get different values of $ f\left( x \right)$. Consider the provided limit, $\underset{x\to -1}{\mathop{\lim }}\,\left| x+1 \right|$. Consider the graph of the function $ f\left( x \right)=\left| x+1 \right|$ . To find $\underset{x\to -1}{\mathop{\lim }}\,\left| x+1 \right|$, examine the portion of the graph near $ x=-1$. As x gets closer to $-1$, the value of $ f\left( x \right)$ gets closer to the y-coordinate of 0. This point $\left( -1,0 \right)$ is as shown in the above graph. The point $\left( -1,0 \right)$ has a y-coordinate of 0. Thus, $\underset{x\to -1}{\mathop{\lim }}\,\left| x+1 \right|=0$. Hence the value of $\underset{x\to -1}{\mathop{\lim }}\,\left| x+1 \right|$ is 0.
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