The diagram shows the Maclaurin series approximation to degree n for the exponential function. The exponential function is shown in red and the Maclaurin series approximation function is shown in blue. Move point A to see the error in the approximation at different points.[br][br]Use the slider to change the value of n.[br][br]You can use the toolbar to zoom in and out, or move the drawing pad to look at different parts of the graph.[br][br]Click the checkbox to look at the values of the derivatives at point A. In particular, compare the values when A has x-coordinate 0.

You can change the function by double-clicking on the definition of f(x) and redefining it.[br][br]For which functions are the approximations good for all values of x?[br]For which functions are the approximations good only for a limited range of values of x?