Devin's Blog

The informal of definition of a limit is “what is happening to x as x gets close to a certain number.” In order for a limit to exist, we must be approaching the same y-value as we approach some value c from either the left or the right side. If this does not happen, we say that the limit does not exist as gets closer to c.

If we want the limit of f’x as we approach some value of c from the left hand side, we will write

The concept of limits as x approaches infinity means the following: “what happens to x as x gets infinitely large.”

We are interested in what is happening to the y-value as the curve gets farther and farther to the right. We can also talk about limits as x approaches negative infinity. This means what is happening to the y-value as the curve gets farther and farther to the left. The terminology we use are the following:

Although we use the term “as x approaches infinity”, realize that x cannot approach infinity as infinity does not exist. The term x approaches infinity” is just a convenient way to talk about the curve infinitely far to the right.

There are only 4 possibilities for a limit the curve can go up forever. In that case, the point on the curve can go down forever. In that case, limit does not exist. For convenience sake, the limit does not exist.