# Infiinity Limit Problem

• Sep 10th 2013, 07:39 PM
Jason76
Infiinity Limit Problem
$\lim x \rightarrow \infty \dfrac{\sqrt{9x^{6} - x}}{x^{3} + 5}$

$\lim x \rightarrow \infty \dfrac{(9x^{6} - x)^{1/2}}{x^{3} + 5}$ (Star)

Hint?

I know that infinity plugged into any $\dfrac{a}{n}$ (where n is a variable to any power) is zero.
• Sep 10th 2013, 09:17 PM
Prove It
Re: Infiinity Limit Problem
There is no such thing as "plugging in infinity" as infinity is not a number. However, you notice that the behaviour of a fraction with an increasing denominator is to get smaller.

Anyway, start by dividing the top and bottom of both fractions by the highest power of x.
• Sep 12th 2013, 10:54 AM
ubhutto
Re: Infiinity Limit Problem
the limit of that equation is 3.
Like prove it said, you should divide by the biggest degree which in this case is 6. when you divide the denominator by 6, be sure to first multiply the 6 * 1/2 as the degree is being taken out of the squareroot.