Limits of Rational Functions - Concept

I want talk about limits of rational functions and by that I mean what happens as x gets larger and larger?
First let's look at two really simple examples; f of x equals 10 over x. What happens as x gets larger and larger? Let's start with a number like 1, 10 over 1 would be 10, how about 10? 10 over 10 is 1. 100, 10 over 100 0.1, how about a 1000? 10 over a 1000 is 0.01. You can see that as x gets larger, that the values of f of x are going to zero. We say as x goes to infinity f of x goes to 0 or we write limit as x approaches infinity of f of x equals 0. This is a kind of notation that you'll see a lot in Calculus.
Let's see what happens to this example, g of x equals 25 over x squared. We'll start again with x=1 we get 25 over 1 squared which is 25, 10 we get 25 over 100 which is 0.25, 100 a 100 squared is 10,000 25 over 10,000 is 0.0025 and you can see that as x is going to infinity, this is going to 0 even faster than the other function and so here again we say limit as x approaches infinity of g of x is 0. Now you can probably gather that this sort of thing is always going to happen. When you have a function like this h of x equals a constant over x to a positive integer power, if that's the kind of a function you have, then the limit as x approaches infinity of h of x is always 0 and it turns out that the limit as x approaches negative infinity of h of x is always 0 and so those are really important facts and we're going to use those to find limits of other rational functions.