Some operations in Math are relatively easy to perform on polynomials, but difficult or impossible to perform on non-polynomial functions.[br][br] A Taylor Polynomial gives a polynomial function [color=#ff00ff]P(x)[/color] that matches a given [color=#0000ff]f(x)[/color]. As more terms are added (increased n value), the match becomes better. Sometimes the match only occurs on a limited "interval of convergence."[br][br]In the early days of studying Taylor Polynomials and Taylor Series, it may help to play with this construction and get a feel of what they are.[br][br]Enter a function [color=#0000ff]f(x)[/color] or use one of the pre-set functions.[br]n determines the degree of the Taylor Polynomial [color=#ff00ff]P(x)[/color].[br]c gives the x-value of the "center" of the Taylor Polynomial [color=#ff00ff]P(x)[/color].[br]x[sub]f[/sub] is the x-coordinate of point A on the [color=#0000ff]f(x)[/color] graph and point B on the [color=#ff00ff]P(x)[/color] graph.[br][br]If there is a finite interval of convergence, where does it appear to begin and end?[br]Set x[sub]f[/sub] at one of the endpoints of the interval of convergence and vary the value of n.[br]Does the Taylor Polynomial seem to converge or diverge at the endpoint?[br][br]____________[br][br][color=#ff0000]Depending largely on your device, GeoGebra may struggle or completely stall if you set the n value too high for certain functions. Of the preset functions, arctan(x) tends to cause problems. You may have to reload the webpage when setting n more than 10 or so.[/color]