# August

Under Revision starting October 16, 2018

Resources  Print and online information

Graphing Calculator Notes for AP Calculus

### Thoughts on Grading and Scaling

On Scaling  Also see “Easier” Exams (7-11-2014)

The Unknown Thing – Why we use x – A TED Talk.

Absolutely Thoughts on Absolute Value

Extremes without Calculus

Show Me the Math!  Was math invented or discovered?

Inequalities  solving inequalities without all the arithmetic

Amortization  Find your monthly payment of a loan. – An application of geometric series (for BC classes)

### ContinuityThe definition of continuity.

Continuity Should continuity come before limits?

From One Side or the Other One-sided limits and one-sided differentiability

How to Tell Your Asymptote from a Hole in the Graph  From the technology series. Showing holes and asymptotes on a graphing calculator.

Fun with Continuity Defined everywhere and continuous nowhere. Continuous only at a single point.

Theorems The Intermediate Value Theorem (IVT) and suggestions on teaching theorems.

Intermediate Weather  Using the IVT

Right Answer – Wrong Question Continuity or continuity “on its domain”?

Asymptotes

Fun with Continuity

Right Answer – Wrong Question. What does “Continuous on its domain” mean.

Far Out  A fun limit, but best saved until after students can find maximum values and points of inflection.

### Limits

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, an important property of functions, depends on limits. All derivatives and all definite integrals are limits. For AP Calculus students need a good intuitive understanding of limits, what they mean, and how to find them The formal (delta-epsilon) definition is not tested and need not be taught, however, do not feel that you have to avoid it. If your students can handle it, let them try.

Why Limits?

Deltas and Epsilons

Finding Limits

Dominance

VIDEOS on Limits

### Theorems, Definitions, and Logic

For Any – For Every – For All

Theorems

Definitions

VIDEOS on Theorems

Revised and updated October 19, 2018.