Chapter 14.2, Problem 12AYU

In Problems 7-42, find each limit algebraically.

$\underset{x\to 4}{\lim }\left(-3x\right)$

To determine

To find: $\underset{x\to 4}{\text{lim}}\left(-3x\right)$

Answer to Problem 12AYU

Solution:

$-12$

Explanation of Solution

Given:

$\underset{x\to 4}{\text{lim}}\left(-3x\right)$

Formula used:

$\underset{x\to \text{ c}}{\text{lim}}\left[f\left(x\right)\cdot \text{ g}\left(x\right)\right]=\underset{x\to \text{ c}}{\text{lim}}f(x)\cdot \underset{x\to \text{ c}}{\text{lim}}\text{g}\left(x\right)$

And,

$\underset{x\to \text{ c}}{\text{lim}}b=b\text{ and }\underset{x\to \text{ c}}{\text{lim}}x=c$

Calculation:

So $\underset{x\to 4}{\text{lim}}-3x=\underset{x\to 4}{\text{lim}}-3\cdot \underset{x\to 4}{\text{lim}}x$.

$=-3\times \left(4\right)$

$=-12$

So $=\underset{x\to 4}{\text{lim}}\left(-3x\right)=-12$.