Where is negative infinity on a graph

So the limit of f of x as we approach six from the left hand side, what is this going to be equal to? So as we approach from the left hand side we can see f of four is a little under two, f of five looks like it's around three, f of 5. Well here, f of seven, it's negative, f of 7. So it looks like this is unbounded in the negative direction, so this is negative infinity. And then we think about as we approach six from the left hand side, we see that we go to positive infinity, and that is this choice right over here, so we rule out that one, and that is what we will pick.

Infinite limits: graphical. In the next chapter we will be interested in "dividing by 0. In other words, we will want to find a limit. These limits will enable us to, among other things, determine exactly how fast something is moving when we are only given position information.

Later, we will want to add up an infinite list of numbers. We will do so by first adding up a finite list of numbers, then take a limit as the number of things we are adding approaches infinity. Surprisingly, this sum often is finite; that is, we can add up an infinite list of numbers and get, for instance, These are just two quick examples of why we are interested in limits.

Many students dislike this topic when they are first introduced to it, but over time an appreciation is often formed based on the scope of its applicability. Gregory Hartman Virginia Military Institute. Solution In Example 4 of Section 1. Solution It is easy to see that the function grows without bound near 0, but it does so in different ways on different sides of 0. Later, we will show how to determine this analytically. Solution Before using Theorem 11, let's use the technique of evaluating limits at infinity of rational functions that led to that theorem.

You won't be taken from this page or asked to login. Article Browser. Infinity and DNE in Limits. Recent Posts See All. Penji Team. January 11, View Profile. Get in Touch. The common mistake is to say that is smaller than 0.

While this may be true according to the natural order on the real line in term of sizes, is big, very big! So when do we have to deal with and? Easy: whenever you take the inverse of small numbers, you generate large numbers and vice-versa.

Mathematically we can write this as:. Do not treat as ordinary numbers. These symbols do not obey the usual rules of arithmetic, for instance, , , , etc. Consider the function.