Maclaurin series approximations
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. Use the slider to change the value of n. You can use the toolbar to zoom in and out, or move the drawing pad to look at different parts of the graph. 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. For which functions are the approximations good for all values of x? For which functions are the approximations good only for a limited range of values of x?