Question

In Problems 13–32, use the accompanying graph of y = f(x).

Does $\underset{x\to 4}{\lim }f\left(x\right)$exist? If it does, what is it?

Short answer

Yes limit exist and$\underset{x\to 4}{\lim }f\left(x\right)=0.$

Step-by-step solution

Step. 1 Given and limit

We are given with the graph of the function and to for the limit to exist LHL = RHL.

Step. 2 Calculating LHL and RHL

From the graph it is clear that,

$\underset{x\to 4^{-}}{\lim }f\left(x\right)=0$and $\underset{x\to 4^{+}}{\lim }f\left(x\right)=0.$

Since LHL = 0 and RHL = 0.

Therefore, the limit of the function exist at $x=4$and it is equal to 0.

$\underset{x\to 4}{\lim }f\left(x\right)=0.$