Question

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

Answer 1

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

Now you have:

`cancel((1,000,000)^2)/(1,000,000)^cancel(3)=1/(1,000,000)~=0`

So you can write:

`lim_(x->oo)(x^2+2)/(x^3-1)=0`