AP Calculus 1 - Limits (Overview and Example Problems)
This video covers all AP Calculus AB standards related to limits and provides an overview of the idea of limits including the following:
Defining Limits
Estimating Limits Graphically and Numerically
Evaluating Limits Algebraically
One-sided Limits
Asymptotes (vertical and horizontal)
Continuity
Limits introduce the subtle distinction between evaluating a function at a point and considering what value the function is approaching, if any, as x approaches a point. This distinction allows us to extend understanding of asymptotes and holes in graphs with formal definitions of continuity.
Consider reviewing rational functions before watching this video. Limits are the foundation for differentiation (instantaneous rate of change), integration (antidifferentiation), and infinite series (covered in Calculus 2). They are the basis for important definitions and for theorems that are used to solve realistic problems involving change and to justify conclusions.