One-sided limits

So, a function may not always have a limit, or it might not exist on both sides of a point.
Let's take for example the logarithm. The logarithm of x is not defined for any x that is zero or negative.
Here's the graph:

Now, for the point x = 0, we can't say that the limit exists, because there is no value that is approaching zero from the left, aka negatives.
This is why the one-sided limits exist. We can however approach zero from the RIGHT, so, the positive x values.

The one-sided limit from the right, or, approaching a point c from elements larger than it, is written with a plus on top of the point we're approaching on the limit symbol: Similarly, the one-sided limit from the left, or, approaching a point c from elements smaller than it, is written with a minus on top of the point we're approaching on the limit symbol:Now look at the graph.
What can you say about:

Answer: It does not exist. There are no values of x approaching 0 from the left for which log(x) exists.

Now, what can you say about:

Answer: As we approach zero from the right, you see that the value of log(x) gets infinitely smaller, the function log(x) diverges to negative infinity. This limit exists and is equal to negative infinity. Let's learn about One-sided limits, and the general limit