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

• Dec 10th 2010, 03:50 PM
RCola
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?
• Dec 10th 2010, 04:25 PM
dwsmith
$\displaystyle \displaystyle \lim_{n\to\infty}\frac{n^{2/3}}{n}=\lim_{n\to\infty}\frac{1}{n^{1/3}}=\frac{1}{\infty}=0$
• Dec 10th 2010, 08:45 PM
aukie
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

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

along with the algebra of limits, i.e. the sum, and product rules etc.
• Dec 11th 2010, 01:04 AM
mr fantastic
Quote:

Originally Posted by dwsmith
$\displaystyle \displaystyle \lim_{n\to\infty}\frac{n^{2/3}}{n}=\frac{1}{n^{1/3}}=\frac{1}{\infty}=0$

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