## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 11 - Section 11.1 - Finding Limits Using Tables and Graphs - Exercise Set - Page 1138: 25

#### Answer

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

#### Work Step by Step

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

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