# Visualizing Taylor polynomial approximations

On pp. 18-23 of the Mathematics Tutorial, I show how y = ex can be approximated with a Taylor polynomial centered at x=0 for $\delta x$ values ranging from -2 to +2.  In his video lesson entitled “Visualizing Taylor polynomial approximations”, Sal Kahn essentially replicates my work; the only difference between Sal’s numerical example and mine is that Sal approximates y = ex 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.