# How do you find the limit of ((x^2 +2)/(x^3-1) as x approaches infinity?

May 22, 2015

Imagine that we use as $\infty$ a values very big such as: $1 , 000 , 000$
Your function, basically, becomes: ${\left(1 , 000 , 000\right)}^{2} / {\left(1 , 000 , 000\right)}^{3}$ the other two numbers $+ 2$ and $- 1$ are irrelevant compared to $1 , 000 , 000$ so you can forget them.

Now you have:

$\frac{\cancel{{\left(1 , 000 , 000\right)}^{2}}}{1 , 000 , 000} ^ \cancel{3} = \frac{1}{1 , 000 , 000} \cong 0$

So you can write:

${\lim}_{x \to \infty} \frac{{x}^{2} + 2}{{x}^{3} - 1} = 0$