“A Little Calculus”

A Little Calculus is an app for iPad and iPhones. While I don’t usually do product reviews, I think this one is so good that I am making an exception. There are many good websites that illustrate calculus concepts. Many of them, however, do not allow teachers to enter their own examples; they must use…

Other Asymptotes

A few days ago, a reader asked if you could find the location of horizontal asymptotes from the derivative of a function. The answer, alas, is no. You can determine that a function has a horizontal asymptote from its derivative, but not where it is. This is because a function and its many possible vertical…

Extreme Polar Conditions

Looking at the graphs of polar curves can be quite fascinating. Doing “calculus” kinds of things is different, yet the same as in Cartesian coordinates. A discussion on the AP Calculus Community here  got me thinking about extreme values of polar functions. The terms maximum and minimum here refers to the value of r(θ) which…

Parametric Equations, Polar Coordinates, and Vector-Valued Functions – Unit 9

Unit 9 includes all the topics listed in the title. These are BC only topics (CED – 2019 p. 163 – 176). These topics account for about 11 – 12% of questions on the BC exam. Comments on Prerequisites: In BC Calculus the work with parametric, vector, and polar equations is somewhat limited. I always…