Limits – They Make the Calculus Work.

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,…

Summer Fun

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…

How to Tell your Asymptote from a Hole in the Graph.

The fifth in the Graphing Calculator / Technology series (The MPAC discussion will continue next week) Seeing discontinuities on a graphing calculator is possible; but you need to know how a calculator graphs to do it. Here’s the story: The number you choose for XMIN becomes the x-coordinate of the (center of) the pixels in the…

Continuity

Limits logically come before continuity since the definition of continuity requires using limits. But practically and historically, continuity comes first. The concept of a limit is used to explain the various kinds of discontinuities and asymptotes. Start by studying discontinuities. Types of discontinuities to consider: removable (a gap or hole in the graph), jump, infinite…