Approximating Functions with Polynomials

Complex functions can often be approximated over a region of their domain by a polynomial. This applet lets you explore this phenomenon for different types of function. Enter a function of your choice in the input box at the top of the screen. Move the yellow dot on the x axis to the region of the domain where you would like the approximation to be good. Slide the slider the choose the order of the approximating polynomial. Some questions to think about- If you place the yellow dot on the origin - where is the polynomial approximation best for the exponential function? - why do the approximating polynomials for sin(x) contain no even powers of x? What other questions could / would you put to your students based on this applet?