Discontinuities of The Second Kind

Let's now take a look at this graph:

Notice that as we approach that point which we'll estimate to be x = 0.25, we approach two different values.
In this discontinuity, the limit of this function does not exist at all.

However, its limits from the left and right do exist!
This is called a "jump" discontinuity.

Here's an exercise for you. From the graph, determine, approximately:

• Answer:
  • a) The limit as x approaches 0.25 from the left is approximately equal to 1.10.
  • b) The limit as x approaches 0.25 from the right is approximately equal to -1.10

Great job. Let's move on to The Uniqueness of The Limit