Good Question 14

Good Question 14 – The Integral Test I have no criteria for what constitutes a “Good Question” for this series of occasional posts. They are just questions that I found interesting, or that seem more than usually instructive, or that I learn something from. I cannot quote this question (2016 BC 92) since it is…

Math vs. the “Real World”

There is a difference between mathematics and the “real world”: In the real world you are allowed to do whatever you want, as long as there is no law against doing it; in mathematics, you cannot do something unless there is a law that says you may. A question that comes up often on the…

Improper Integrals and Proper Areas

A few years ago on the old AP Calculus discussion group a teachers asked a question about this improper integral:   His (quite perceptive) student pointed out that the range of the inverse tangent function is arbitrarily restricted to the open interval . The student asked if some other range would affect the answer to…