Karl Weierstrass (1815 – 1897) was the mathematician who (finally) formalized the definition of continuity. Included in that definition was the epsilon-delta definition of limit. This definition has been pulled out, so to speak, and now is usually presented on its own. So, which came first – continuity or limit? The ideas and situations that…
In an ideal world, I would like to have all students study limits in their pre-calculus course and know all about them when they get to calculus. Certainly, this would be better than teaching how to calculate derivatives in pre-calculus (after all derivatives are calculus, not pre-calculus). Limits are the foundation of the calculus. Continuity,…
August and the school year is about to start! As I did last year, this year my weekly posts will point you to previous posts on topics that will be coming up a week or two later. I try to stay a little ahead of you so you’ll have time to read them and incorporate…
Every Spring I have a lot of fun proofreading Audrey Weeks’ new Calculus in Motion illustrations for the most recent AP Calculus Exam questions. These illustrations run on Geometers’ Sketchpad. In addition to the exam questions Calculus in Motion (and its companion Algebra in Motion) include separate animations illustrating most of the concepts in calculus…
In this post we look at another part of the AP Calculus BC exam. Good Question 15 discussed the unusual units in 2018 BC 2(a). In this post we look at 2018 BC 2(b) where units help us find the correct integral to answer the question. How do you answer a question of a type…
My choices for the Good Question series are somewhat eclectic. Some are chosen because they are good, some because they are bad, some because I learned something from them, some because they can be extended, and some because they can illustrate some point of mathematics. This question and the next, Good Question 16, are in…
Best wishes to everyone tomorrow. Hope your students do well!
