Question

In Problems 7– 42, find each limit algebraically

$\underset{x\to 2}{\lim }\left(5x^4\right)$

Short answer

The value of the limit$\underset{x\to 2}{\lim }\left(5x^4\right)=80.$

Step-by-step solution

Step 1. Given Information

The given limit and function is$\underset{x\to 2}{\lim }\left(5x^4\right)$

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,

$$\begin{gathered} \underset{x\to 2}{\lim }\left(5x^4\right)=5·2^4 \\ =5\times 16 \\ =80 \end{gathered}$$