Taylor Polynomials
Some operations in Math are relatively easy to perform on polynomials, but difficult or impossible to perform on non-polynomial functions.
A Taylor Polynomial gives a polynomial function P(x) that matches a given f(x). As more terms are added (increased n value), the match becomes better. Sometimes the match only occurs on a limited "interval of convergence."
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.
Enter a function f(x) or use one of the pre-set functions.
n determines the degree of the Taylor Polynomial P(x).
c gives the x-value of the "center" of the Taylor Polynomial P(x).
xf is the x-coordinate of point A on the f(x) graph and point B on the P(x) graph.
If there is a finite interval of convergence, where does it appear to begin and end?
Set xf at one of the endpoints of the interval of convergence and vary the value of n.
Does the Taylor Polynomial seem to converge or diverge at the endpoint?
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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.