[math]T_n(x)[/math] is the [math]n^{th}[/math] Taylor Polynomial of [math]f(x)[/math] 1) Drag the point [math]x_0[/math] along the [math]x[/math]-axis to change the center of expansion. 2) Slide [math]n[/math] to change the degree. 3) Enter a new function in the text box to change the function.

[b]Taylor's Theorem[/b]: There exists [math]\xi[/math] between [math]x[/math] and [math]x_0[/math] such that [math]f(x)-T_n(x)=R_n(x)[/math] where [math]R_n(x)=\frac{f^{n+1}(\xi)}{(n+1)!}(x-x_0)^{n+1}[/math]