Quiz 4 will cover the following topics.
- Limits of Functions
- \(\epsilon\)-\(\delta\) definition of limit
- Other characterizations of limits (sequential and topological)
- Limits rules (addition, multiplication, etc.)
- Continuous Functions
- Definition of continuity at a point and on a set
- Other characterizations of continuity (sequential and topological)
- Continuity rules (addition, multiplication, and composition)
- Pre-images of open sets are open
- Pre-images of closed sets are closed
- Properties of Continuous Functions
- Images of compact sets are compact
- Images of bounded sets are bounded
- Images of connected sets are connected
- Extreme Value Theorem (a continuous function achieves its maximum and minimum values on any compact domain)
- Intermediate Value Theorem