Question

In Problems 7– 42, find each limit algebraically

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

Short answer

The value of the limit$\underset{x\to 4}{\lim }(-3x)=-12$

Step-by-step solution

Step 1. Given Information

The given limit and the function is$\underset{x\to 4}{\lim }(-3x)$

We need to find the given limit.

Step 2. Expanding the limit 

We know,

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

Therefore,

role="math" localid="1646939599725" $\underset{x\to 4}{\lim }(-3x)=\left[\underset{x\to 4}{\lim }(-3)\right]\left[\underset{x\to 4}{\lim }x\right]$

Step 3. Applying limits

The obtained expression is

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

$$\begin{gathered} =[-3]\left[4\right] \\ =-12 \end{gathered}$$