Evaluating Limits

A limit is the point at wich two lines will intersect and stop or a point wich a line will no longer increase or decrease. They can neither continue on because both lines are in eachothers way. Limits tell us where we can start a graph but we need to know how to find them. That is where 3 simple rules come into play. 

These all tell us how to find our limits. But wait there is a trick. You must start with substitution to begin with. Trust me it will make you life much easier. If you plug in a number and get a nember that is not 0/0 then that is your limit. If it is 0/0 then that is the intermediate form and you have to use the other two methods. 

CANCELLLATION TECHNIQUE

This is where you try to cancle out a part of an equation from either the top or bottom so it will no longer equal 0. This is just factoring and solving. Here are two examples

The next technique is more confusing and harder. 

RATIONALIZATION TECHNIQUE

This is when there is a radical in the equation. First check to make sure there is an intermediate form. If there is then you must find the conjugate of the rational. If it is 4+rad8 then the conjugate is 4-rad8. Here are a couple examples. 

Now there is a tech ique to find out what the limit is if two lines are approaching one another and either have a pont for a limit or do not have limits. This is where one uses the one sided limit form. 

Here is an example of this.