When are we ever …

The following answer to a question we’ve all been asked was posted yesterday on a private Facebook page for AP Calculus readers. The author, Allen Wolmer is a teacher and AP Calculus reader. He teaches at Yeshiva Atlanta High School, in Atlanta, Georgia. I reprint it here with his kind permission. Thank you Allen.     A…

Determining the Indeterminate

The other day someone asked me a question about the implicit relation . They had been asked to find where the tangent line to this relation is vertical. They began by finding the derivative using implicit differentiation: The derivative will be undefined when its denominator is zero. Substituting y = 0 this into the original…

Riemann Sums

In our last post we discussed what are called Riemann sums. A sum of the form  or the form (with the meanings from the previous post) is called a Riemann sum. The three most common are these and depend on where the is chosen. Left-Riemann sum, L, uses the left side of each sub-interval, so…