# Math Help - What is the steps of getting result of limit of the function?

1. ## What is the steps of getting result of limit of the function?

Limit[((n^2 - n)^(1/3))/(n + 2), n -> Infinity] == 0

Why answer is equals to 0? What are the steps?

2. $\displaystyle \lim_{n\to\infty}\frac{n^{2/3}}{n}=\lim_{n\to\infty}\frac{1}{n^{1/3}}=\frac{1}{\infty}=0$

3. The trick (or first step) to all these types of limit calculations is to divide the top and bottom by the highest power of n, and then use the fact

$\lim_{n\to \infty } \, \frac{1}{n^a}=0, a>0$

along with the algebra of limits, i.e. the sum, and product rules etc.

4. Originally Posted by dwsmith
$\displaystyle \lim_{n\to\infty}\frac{n^{2/3}}{n}=\frac{1}{n^{1/3}}=\frac{1}{\infty}=0$
I hope what you meant to post is $\displaystyle \lim_{n\to\infty}\frac{n^{2/3}}{n}= \lim_{n\to\infty} \frac{1}{n^{1/3}} =0$.