Taylor polynomial
A function of your choice is given. (You can change the function by typing in the input box: the graph of the function f is shown in blue.)
Select a point on the graph of f. The point is shown in red. The x-coordinate of this point will be the center of the Taylor series. (You can, of course, leave the point in its default location.)
Choose the value of "n" using the slider. This will be the order of the Taylor polynomial. The graph of the Taylor polynomial y=T(x) will be shown in red. Notice that when "n" is bigger, the red graph is "a lot more like" the blue graph. Keep in mind that the red graph is a polynomial, whereas the blue graph can be any function that can differentiated "n" times.
(If we could only keep increasing "n" to be "infinity", we would then in red have a Taylor series instead of a Taylor polynomial.)