Limits and Continuity – Unit 1

This is a re-post and update of the first in a series of posts from last year. It contains links to posts on this blog about the topics of limits and continuity for your reference in planning. Other updated post on the 2019 CED will come throughout the year, hopefully, a few weeks before you…

Which Came First?

In one of my math classes – it may have been calculus – many decades ago, we started by determining what kind of functions we were going to study. A good part of the answer was continuous functions. Looking closely, you will find that almost all the theorems in beginning calculus require that the function…

Continuity

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…

Continuity

Karl Weierstrass (1815 – 1897) was the mathematician who (finally) formalized the definition of continuity. In that definition was the definition of limit. So, which came first – continuity or limit? The ideas and situations that required continuity could only be formalized with the concept of limit. So, looking at functions that are and are…

From One Side or the Other.

Recently, a reader wrote and suggested my post on continuity would be improved if I discussed one-sided continuity. This, along with one-sided differentiability, are today’s topic. The definition of continuity requires that for a function to be continuous at a value x = a in its domain  and that both value are finite. That is, the…