Question

In Problems 8–12, use the accompanying graph of$y=f\left(x\right)$

Does $\underset{x\to 1}{\lim }f\left(x\right)$exist? If so, what is it? If not, explain why not?

Short answer

The limit exists that is$\underset{x\to 1}{\lim }f\left(x\right)=2$

Step-by-step solution

Step 1. General formula

The value of a limit is found by using,

$\underset{x\to c^{-}}{\lim }f\left(x\right)=\underset{x\to c^{+}}{\lim }f\left(x\right)=\underset{x\to c}{\lim }f\left(x\right)$

It is clear from the graph,

$$\begin{gathered} \underset{x\to 1^{-}}{\lim }f\left(x\right)=2 \\ \underset{x\to 1^{+}}{\lim }f\left(x\right)=2 \end{gathered}$$

Step 2. Value of the limit

We have found that,

$\underset{x\to 1^{-}}{\lim }f\left(x\right)=2=\underset{x\to 1^{+}}{\lim }f\left(x\right)$

Therefore,

$\underset{x\to 1}{\lim }f\left(x\right)=2$