Question

find the limit.

$\underset{x\to \infty }{\lim }\frac{3}{x^4}$

Short answer

The value of limit of the given function is $0.$

Step-by-step solution

Step 1. Given information.

The limit of function is given here,

$\underset{x\to \infty }{\lim }\frac{3}{x^4}$

Step 2. Formula used.

Here, in the given question we apply the concept:

If $k$is any positive integer, then

$\underset{x\to \infty }{\lim }\frac{1}{x^k}=0$

Step 3. Simplification.

Given, $\underset{x\to \infty }{\lim }\frac{3}{x^4}$

Here, first we apply limit of constant multiple.

After it we apply the value of $x$which is equals to $\infty .$

$\begin{array}{c}\underset{x\to \infty }{\lim }\frac{3}{x^4}=\underset{x\to \infty }{\lim }\left(3\times \frac{1}{x^4}\right)\\ =3\underset{x\to \infty }{\lim }\left(\frac{1}{x^4}\right)\\ =3\times 0\\ =0\end{array}$

Therefore, our final answer is$0.$