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.

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 ...