Question

Graph each function. Use the graph to find the indicated limit, if it exists.

$\underset{x\to \mathrm{\pi }}{\lim }f\left(x\right),f\left(x\right)=\cos \left(x\right)$

Short answer

The limit is$-1$.

Step-by-step solution

Step 1. Given Information  

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

Step 2. Plotting the graph 

So, the graph of the function $x=\mathrm{\pi }$is

Step 3. Finding the limit   

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

$$\begin{gathered} f\left(x\right)=\cos \left(x\right) \\ \Rightarrow f\left(\mathrm{\pi }\right)=\cos \left(\mathrm{\pi }\right) \\ \Rightarrow f\left(\mathrm{\pi }\right)=-1 \\ \therefore \underset{x\to \mathrm{\pi }}{\lim }f\left(x\right)=-1 \end{gathered}$$