Limits

Imagine you're on a plane.
You know, the air gets thinner and thinner so your plane can only get so high.

Now imagine you're running. Sometimes you can run forever, sometimes you can run into a wall.

Now imagine you have an air conditioner, but it can only heat up your room so much. Or cool it down.

In all these cases and infinitely many more, you hit a limit.

Limits are related to the concepts of Convergence, Divergence and Indeterminacy.

Let's talk about convergence.

When we discussed convergence a while ago, we said that a function or sequence converges when it gets ever so close to a point. Sometimes it touches this point, sometimes it gets infinitely closer to it without ever actually touching it.

This is exactly what a limit is: In mathematical notation, this "limit as x tends to c is equal to L" is written as:

Now, what happens when we have instead, divergence?

When we discussed divergence, we established that a function or sequence diverges, when as we get ever so close to an input value, our outputs does not "converge". It does not "approach" a point. Instead, it gets further away from it.
So, it gets infinitely further and further away from it.

In our new terms of limits, we now have that this limit is equal to either infinity.

What about indeterminates?

As you have probably figured out, if said function is indeterminate, this limit does not exist.

That's how easy it is.

Let's learn about One-sided limits