# Limits and Differential Calculus

The study of limits is a very important one in  calculus . Limits are used to form the base of the derivative, which is arguably one of the most important aspects of  calculus . There are many different rules you need to follow when taking limits. It will take some time to truly understand what a limit is, but this is worth the effort. Having a good knowledge of limits will really help you with differential  calculus  studies.

Roughly speaking, we say that values of f(x) get closer and closer to the number L as X gets closer and closer to the number a. The statement is true from either side of a, but x cannot equal a. There is a more precise definition for limit but it will be seen in future studies.

So this may seem like a limit is simply the value of the function at a given point. This is really not the case. A function does not even have to be defined at a specific point for it to have a limit there. For example you can have a simple polynomial with an open point, but a limit will still exist at that open point. But obviously the value of the limit will not be the value of the open point, which may even be completely undefined.

It is much easier to see how limits behave graphically. For most normal functions finding the limit will be very straightforward. We can simply use the direct substitution property. The direct substitution property says that the value of the limit is simply the value of the function at the limit point. It is important to note that you can only use the direct substitution property for polynomials and rational functions.

Limits may seem confusing at first, but once she tried several of them they will not be that hard. Practice them now, as you will be seeing a lot more of them in this definition of the derivative section.