TI-89 Animation of Taylor Approximations

The TI-89 program below will generate Taylor polynomials to approximate a function y1(x).  It is assumed that y1(x) has been stored in the calculator.

NOTE:  Because of graphing/labeling limitations on a graphing calculator screen, we recommend that this routine be used as an in-class demo with a significant amount of instructor dialog to explain the action.

The user makes the following inputs during program execution:

  • the plotting interval [a,b]

  • the range interval [c,d]

  • the maximum degree of Taylor polynomial to be graphed, M

  • the center of the approximation

  • an option to display the function and the Taylor polynomials of degree N = 0 to M OR display, in a split screen,  the function with the Taylor polynomials on the left and the error function on the right.

Note that two plotting options are available.  The first shows y1(x) and the Taylor polynomials on a single graph.  An animations illustrating program execution under this option is shown below. 

No error displayed

The second option splits the screen into two graphing windows.  On the left, the graph of y1(x) is shown together with the Taylor polynomial.   The right  window is a graph of the error function, calculated as y1(x) - g(x), where g(x) is the Taylor polynomial of degree N.  Note that the horizontal graphing scales are the same, however, the vertical scales may be quite different.

Split graphing screen; error function displayed on right.

In each option, execution pauses after the graphs are complete.  Execution continues to calculate and plot the Taylor polynomials of degree 0 to M, where M is the maximum degree, an input variable.

The TI-89 program is shown below.  Follow the link at the bottom of the page to download the program.

Download the TI-89 program here.  After downloading to your computer, if you have TI-Graph Link cable and application, you can download directly to your calculator.