The circumference of a sphere is measured to be 24 cm, with a possible error of 0.25 cm. Use the differential \(dV\) to estimate the maximum error in the calculated ...

I've been grading calculus exams this week, and even though my students did quite well overall there were a couple of errors that I see every semester. Errors that make mathematicians' heads explode.

Grade school math students are likely familiar with teachers admonishing them not to just guess the answer to a problem. But a new proof establishes that, in fact, the right kind of guessing is ...

The area \(A\) of a square of side length \(s\) is \(A=s^2\text{.}\) Suppose \(s\) increases by an amount \(\Delta s=ds\text{.}\) Draw a square and then illustrate ...