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

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

- Dec 10th 2010, 03:50 PMRColaWhat 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 PMdwsmith
$\displaystyle \displaystyle \lim_{n\to\infty}\frac{n^{2/3}}{n}=\lim_{n\to\infty}\frac{1}{n^{1/3}}=\frac{1}{\infty}=0$

- Dec 10th 2010, 08:45 PMaukie
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 AMmr fantastic