Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Taylor series error term - graphical representation

  1. Nov 3, 2012 #1
    Hello all,
    Recently I've found something very interesting concerning Taylor series.
    It's a graphical representation of a second order error bound of the series.
    Here is the link: http://www.karlscalculus.org/l8_4-1.html [Broken]

    My question is: is it possible to represent higher order error bounds in a similar way?
    For example: third order error term would have "3! = 6" in a denominator...
    I know that Taylor series is based on Mean Value Theorem and I know the proof of it.
    However it would become much clearer if it was possible to represent error bounds in a graphical way.

    Have a nice weekend.
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 3, 2012 #2

    lurflurf

    User Avatar
    Homework Helper

    Yes, see any calculus book, or this

    http://mathworld.wolfram.com/SchloemilchRemainder.html

    It follows from the mean value theorem

    Often in simple examples the error is well approximated by the next term as in

    [tex]\sin(x) \sim \sum_{k=0}^\infty \frac{x^k}{k!} \sin\left(
    x+k \frac{\pi}{2}\right)[/tex]
     
    Last edited: Nov 3, 2012
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Taylor series error term - graphical representation
  1. Taylor series (Replies: 7)

  2. Taylor series (Replies: 5)

Loading...