Question

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

Short answer

The limit does not exist.

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 $4$of $f\left(x\right)$.

The graph of the function reaches a removable discontinuity when $x$approaches to $4$from the left as well as when$x$approaches to$2$from the right.

From the graph, we can clearly see that $f$approaches to $4$from the left and to $2$from the right as $x$approaches to $4$.

The value of the function from the left and right limits does not coincide.

Therefore, the limit does not exist.