This Mathematica notebook generates the nth Taylor Polynomials centered at x = a for the function y = f(x).  Graphs of the given function and the polynomials are generated. In addition, the remainders (error) are computed and plots are constructed.    

Enter the function of your choice by changing the assignment for f[x].  Change the value of a to change the center.  Note that your choice could affect the intervals over which you need to display the plot.


For trigonometric functions, the graph looks nicer if symbolic rather than decimal-valued tick placements on the graph are used.  If f(x) is a trigonometric function, use TrigTicks for the Tick argument in the calls to Plot.  For non-trigonometric functions, use NonTrigTicks.  In each case, change the tick marks as appropriate.  In addition, change the PlotRange as appropriate for the particular function you use.


Display the graphs of y = f[x] and the ith Taylor Polynomial.  Change the counter increment as appropriate.  



Display the graphs of y = f[x] and the ith Taylor Polynomial together with the ith remainder. Change the counter increment as appropriate.



Mathematica Notebook by
Elizabeth Carver and
Dr. Lila F. Roberts
Mathematics and Computer Science Department
Georgia Southern University
Statesboro, GA  30460

Converted by Mathematica      April 11, 2001