Question

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

Short answer

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

Step-by-step solution

Step 1. Given information

The given limit 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,

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

Therefore,

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