Unlimited

Or When is a limit not a limit? I was discussing the definition of a limit equal to infinity with someone recently. It occurred to me that such functions have no limit! Of course, you say that’s why – sometimes – we say “infinity”. But should we? What does “∞” mean? The definition we were…

Unit 1 – Limits and Continuity

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…

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…

Good Question 17

A common question in (older?) textbooks is to give students a function or relation and have them graph it without technology (because in the old days technology was not available). Students had to find all the appropriate information without hints or further direction: they were supposed to know what to do and do it. AP…