What is a limit modules
After completing this section, students should be able to do the following.
- Consider values of a function at inputs approaching a given point.
- Understand the concept of a limit.
- Use limits to understand local behavior of functions.
- Calculate limits from a graph (or state that the limit does not exist).
- Understand possible issues when estimating limits using nearby values.
- Define a one-sided limit.
- Explain the relationship between one-sided and two-sided limits.
- Distinguish between limit values and function values.
- Identify when a limit does not exist.
- Define continuity in terms of limits.
- Use the continuity of famous functions (on their domains) when computing limits.
Stars and functions
Two young mathematicians discuss stars and functions.
What is a limit
We introduce limits.
The limit of a continuous function at a point is equal to the value of the function at that point.