Question

In Problems 7– 42, find each limit algebraically

$\underset{x\to -2}{\lim }\left(5x\right)$

Short answer

The value of the limit$\underset{x\to -2}{\lim }\left(5x\right)=-10$

Step-by-step solution

Step 1. Given Information

The limit and the function is given as$\underset{x\to -2}{\lim }\left(5x\right)$

We need to find the value of the limit of given function

Step 2. Value of 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,

$\underset{x\to -2}{\lim }\left(5x\right)=\left[\underset{x\to -2}{\lim }5\right]\left[\underset{x\to -2}{\lim }x\right]$

Now, $\underset{x\to c}{\lim }b=b\{b=cons\tan t\}$and $\underset{x\to c}{\lim }x=c$

Therefore,

$$\begin{gathered} \left[\underset{x\to -2}{\lim }5\right]\left[\underset{x\to -2}{\lim }x\right] \\ =\left[5\right][-2] \\ =-10 \end{gathered}$$