Taylor Series Approximations

A Taylor polynomial approximation is based at the point below. You can move the point around and change the function. The higher the degree, the more accurate your approximation is and the wider the interval of accuracy is. Drag the point around, play with the degree of accuracy, and change the interval radius to see what happens to the average error over that interval.

Average Error
14.6709
f(x)=exf(x) = e^x
P3(x)=1+x+12x2+16x3P_{3}(x) = 1 + x + \frac{1}{2}x^{2} + \frac{1}{6}x^{3}
Display Options
3
2.0