This blog entry provides a helpful follow-up for a couple of calculus-related topics that we covered during the Mathematics Tutorial.

- See page 12 of the above-referenced lecture note. There, the equation for a parabola () appears, and the claim that
*dy/dx = 2x*is corroborated by solving the following expression: .In the 11-minute Khan Academy video at https://youtu.be/HEH_oKNLgUU, Sal Kahn takes on the solution of this problem in a very succinct and easy-to-comprehend fashion. - On pp. 18-23 of the Mathematics Tutorial, I showed how
*y =**e*^{x}can be approximated with a Taylor polynomial centered at*x*=0 for values ranging from -2 to +2. In his video lesson entitled “Visualizing Taylor polynomial approximations”, Sal Kahn essentially replicates the work I did; the main difference between my example and Sal’s example is that Sal approximates*y =**e*^{x}with a Taylor polynomial centered at*x*=3 instead of*x*=0. The important insight provided in both cases is that the accuracy of Taylor polynomial approximations increases as the order of the polynomial increases.