Question

find the limit.

$\underset{x\to \infty }{\lim }\frac{6}{x}$

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,

$\underset{x\to \infty }{\lim }\frac{6}{x}$

Step 2. Formula used.

Here, in the given question we apply the formula:

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

Step 3. Simplification.

Given,$\underset{x\to \infty }{\lim }\frac{6}{x}$

Here, first we apply limit of constant multiple.

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

$\begin{array}{c}\underset{x\to \infty }{\lim }\frac{6}{x}=\underset{x\to \infty }{\lim }\left(6\times \frac{1}{x}\right)\\ =6\underset{x\to \infty }{\lim }\left(\frac{1}{x}\right)\\ =6\times 0\\ =0\end{array}$

Therefore, our final answer is $0.$