Limits and Continuity

Guided Notes for this lecture

In this section we will look at how we we define "closeness". What happens when we approach something, but never actually reach it..

For any value of x, we can consider what happens when we get close from the left or close from the right. Also, what happens if those are the same, or if they are different.

We also want to consider what analyzing a limit with a graph might tell us.

For many functions we work with, we need to condiser where and when that function is continuous to determine how we do our analysis.

As we consider the continuity of various functions, we find that some types of functions have continuity patterns we can then use if we recognize the function.

At the end of this section you should be able to answer the following questions:

1. What does it mean to be "close" to a value?
2. How does the notation change if take a limit from the left or right?
3. How can limits help us determine if a function is continuous?

Check Your Understanding
You should try these problems before reviewing the solutions to to these non-graded practice problems.