Question

In Problems 43–52, find the limit as x approaches c of the average rate of change of each function from c to x.

$c=2;f\left(x\right)=5x-3.$

Short answer

The answer is 5.

Step-by-step solution

Step. 1 Given Information

$$\begin{gathered} c=2; \\ f\left(x\right)=5x-3. \end{gathered}$$

Step. 2 Average rate of change of f.  

The average rate of change of f from 2 to x is

$$\begin{gathered} \frac{∆y}{∆x}=\frac{f\left(x\right)-f\left(2\right)}{x-2}=\frac{(5x-3)-7}{x-2} \\ =\frac{5x-10}{x-2}=\frac{5(x-2)}{(x-2)}=5. \end{gathered}$$

Step. 3 Finding limit  

The limit of the average rate of change is

$\underset{x\to 2}{\lim }\frac{∆y}{∆x}=\underset{x\to 2}{\lim }\left(5\right)=5.$