Defining Limits and Using Limit Notation
What is a limit?
One-sided limits
- •
- •
The two-sided limit exists if and only if both one-sided limits exist and are equal
Example: piecewise function
- •
- •
- •
- •
Notation summary
When does a limit NOT exist?
- •
- •
- •
Graphical interpretation
Common mistake
Practice patterns
- •
- •
- •
- •
Vocabulary
Unit 1 topics
Unit 1 overview11.1 Introducing Calculus: Can Change Occur at an Instant?21.2 Defining Limits and Using Limit Notation31.3 Estimating Limit Values from Graphs41.4 Estimating Limit Values from Tables51.5 Determining Limits Using Algebraic Properties61.6 Determining Limits Using Algebraic Manipulation71.7 Selecting Procedures for Determining Limits81.8 Determining Limits Using the Squeeze Theorem91.9 Connecting Multiple Representations of Limits and Continuity101.10 Types of Discontinuities, Infinite Limits, and the IVT