CONTINUITY To help understand limits it is a good idea to look at functions that are not continuous. Historically and practically, continuity should come before limits. On the other hand, the definition of continuity requires knowing about limits. So, I list continuity first. The modern definition of limit was part of Weierstrass’ definition of continuity.
Continuity (8-21-2013) The definition of continuity.
Continuous Fun (10-13-2015) A fuller discussion of continuity and its definition
Right Answer – Wrong Question (9-4-2013) Is a function continuous even if it has a vertical asymptote?
Asymptotes (8-15-2012) The graphical manifestation of certain limits
Fun with Continuity (8-17-2012) the Diriclet function
Far Out! (10-31-2012) When the graph and dominance “disagree” From the Good Question series
Why Limits? (8-1-2012)
Deltas and Epsilons (8-3-2012) Why this topic is not tested on the AP Calculus Exams.
Finding Limits (8-4-2012) How to…
Dominance (8-8-2012) See limits at infinity
Determining the Indeterminate (12-6-2015) Investigating an indeterminate form from a differential equation. From the Good Question series.
Locally Linear L’Hôpital (5-31-2013) Demonstrating L’Hôpital’s Rule (a/k/a L’Hospital’s Rule)
L’Hôpital’s Rules the Graph (6-5-2013)