Truncation Error in Taylor Series

Taylor series for transcendental functions have an infinite number of terms. This Demonstration shows the truncation error created by using a finite number of terms in approximating three such functions with Taylor series based at zero.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The general form of a Taylor series is
assuming the function and all its derivatives exist and are continuous on an interval centered at and containing .
Here are the Maclaurin series (a special case of a Taylor series written around the point ) for the three functions considered:
In this Demonstration, we show the truncation error as a function of the number of terms of the Maclaurin series for the particular value of the function argument.
1. For what values of would the given Maclaurin series for diverge?
2. How would you choose the number of terms to get the value of correct up to a specified number of significant digits?
3. The other source of error in numerical methods is round-off error. What influence does this have on the accuracy of the approximations?
[1] A. K. Kaw, D. Nguyen, and E. E. Kalu, Numerical Methods with Applications, 2010. http://numericalmethods.eng.usf.edu/publications_book.html.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+