Question

Graph each function. Use the graph to find the indicated limit, if it exists.$\underset{x\to 4}{\lim }f\left(x\right),f\left(x\right)=3\sqrt{x}$

Short answer

The limit is$6$.

Step-by-step solution

Step 1. Given Information   

We are given a function $f\left(x\right)=3\sqrt{x}$and we need to graph the function and find $\underset{x\to 4}{\lim }f\left(x\right)$.

Step 2. Plotting the graph   

So, the graph of the function $f\left(x\right)=3\sqrt{x}$is

Step 3. Finding the limit    

To find the value of $\underset{x\to 4}{\lim }f\left(x\right)$we need to find the value of the function at $x=4$.

$$\begin{gathered} f\left(x\right)=3\sqrt{x} \\ \Rightarrow f\left(4\right)=3\sqrt{4} \\ \Rightarrow f\left(4\right)=6 \\ \therefore \underset{x\to -1}{\lim }f\left(x\right)=6 \end{gathered}$$