Question

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

Does $\underset{x\to 0}{\lim }f\left(x\right)$exist? If it does, what is it?

Short answer

Yes it exist and$\underset{x\to 0}{\lim }f\left(x\right)=3.$

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,

$\underset{x\to 0^{-}}{\lim }f\left(x\right)=3and\underset{x\to 0^{+}}{\lim }f\left(x\right)=3$

Since LHL = 3 and RHL = 3.

Therefore, the limit of the function exist at $x=0$and it is equal to 3.

$\underset{x\to 0}{\lim }f\left(x\right)=3.$