Taylor Polynomials vs Least Squares Fits

This interactive applet can be used (if you are in RStudio) to investigate the differences between Taylor Polynomial and Least Squares approximations to functions.

mTaylor(exp(-0.2 * x) * sin(x) ~ x, xlim = c(0, 10))

One could also study other measures of fit, like MISE (mean integrated squared error), or its square root (RMS).