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Q. 29

Expert-verified
Found in: Page 876

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# Graph each function. Use the graph to find the indicated limit, if it exists. $\underset{x\to \frac{\mathrm{\pi }}{2}}{\mathrm{lim}}f\left(x\right),f\left(x\right)=\mathrm{sin}\left(x\right)$

The limit is $1$.

See the step by step solution

## Step 1. Given Information

We are given a function $f\left(x\right)=\mathrm{sin}\left(x\right)$ and we need to graph the function and find $\underset{x\to \frac{\mathrm{\pi }}{2}}{\mathrm{lim}}f\left(x\right)$.

## Step 2. Plotting the graph

So, the graph of the function $f\left(x\right)=\mathrm{sin}\left(x\right)$ is

## Step 3. Finding the limit

To find the value of $\underset{x\to \frac{\mathrm{\pi }}{2}}{\mathrm{lim}}f\left(x\right)$ we need to find the value of the function at $x=\frac{\mathrm{\pi }}{2}$.

$f\left(x\right)=\mathrm{sin}\left(x\right)\phantom{\rule{0ex}{0ex}}⇒f\left(\frac{\mathrm{\pi }}{2}\right)=\mathrm{sin}\left(\frac{\mathrm{\pi }}{2}\right)\phantom{\rule{0ex}{0ex}}⇒f\left(\frac{\mathrm{\pi }}{2}\right)=1\phantom{\rule{0ex}{0ex}}\therefore \underset{x\to \frac{\mathrm{\pi }}{2}}{\mathrm{lim}}f\left(x\right)=1$