Maclaurin polynomials
This applet plots the graphs of e^x, sin x, cos x, ln(1+x), 1/(1-x), (1+x)^(1/2), atctg x, arcsin x and their Maclaurin polynomials up to the 10th order. It demonstrates how well do Maclaurin polynomials approximate the corresponding functions in some neighbourhood of 0.
Explore changing the values of n for the first six functions. What do you notice? What do you think is happening?