Question

In Problems 7– 42, find each limit algebraically

$\underset{x\to -3}{\lim }\left(2x^3\right)$

Short answer

The value of the limit $\underset{x\to -3}{\lim }\left(2x^3\right)$is$-54.$

Step-by-step solution

Step 1. Given Information

The given limit and function is$\underset{x\to -3}{\lim }\left(2x^3\right)$

We need to find the value of the limit.

Step 2. Value of the limit

We know,

$\underset{x\to c}{\lim }\left(a{x}^n\right)=a{c}^n$

Therefore,

$$\begin{gathered} \underset{x\to -3}{\lim }\left(2x^3\right)=2·(-3{)}^3 \\ =2\times -27 \\ =-54 \end{gathered}$$