Ok so here is the limit:

(x->∞)

Now I know that the limit does not really exist, because the degree of the numerator is greater than the degree of the denominator. And this is the answer that they have on my handout.

But I was wondering, would this be considered an infinite limit at infinity as in

∞

(x->∞)

Is the above not true?

And if not, how can I tell when the limit does not exist as above and when it should be infinity. I know that all polynomial functions have infinite limits at infinity. But there are rational limits that I know have infinite limits at infinity as well, such as:

∞

(x->∞)

This one I know is true.

I have a test in the morning on this, so anyone that could add some input that will help clarify this for me in the next 6 hours would be greatly appreciated.