Question

Use the graph shown to determine if the limit exists. If it does, find its value.

Short answer

The value is$\underset{x\to 2}{\lim }f\left(x\right)=2$.

Step-by-step solution

Step 1. Given Information 

We are given the graph and we need to determine if the limit exists and find its value.

Step 2. Finding the limit 

We need to find the limit of the function as $x$approaches to $2$of $f\left(x\right)$.

The graph of the function reaches a removable discontinuity when $x$approaches to $2$.

From the graph, we can clearly see that $f\left(x\right)$approaches $2$as $x$approaches to $2$.

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