Results 1 to 2 of 2

Math Help - Calculate error using Lagrange formula

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    16

    Calculate error using Lagrange formula

    I'm sorry for posting so much but I have another question.
    The problem says:

    let f(x) = sin(x).
    Use the Lagrange formula to find the smallest value of n so that the nth degree Taylor polynomial for f centered at x = 0 approximates f at x = 1 with an error of no more that 0.001.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by etha View Post
    I'm sorry for posting so much but I have another question.
    The problem says:

    let f(x) = sin(x).
    Use the Lagrange formula to find the smallest value of n so that the nth degree Taylor polynomial for f centered at x = 0 approximates f at x = 1 with an error of no more that 0.001.
    The Lagrange form for the remainder is:

    R_n=\frac{x-x_0}{(n+1)!}f^{(n+1)}(\xi),\ \ \xi\in [x_0,x],

    so in this case

    |R_n|=\frac{1}{(n+1)!}|f^{(n+1)}(\xi)|,\ \ \xi\in [0,1],.,

    where |f^{(n+1}(\xi)|\le 1 if n is even and |f^{(n+1}(\xi)|\le \sin(1) if n is odd.

    So now you have to find the smallest n such that:

     <br />
|R_n|\le 0.001<br />

    You should do this seperately for odd and even n, and then select the smallest
    of the two.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Lagrange Error/Taylor's Theorum
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 18th 2010, 02:14 PM
  2. Lagrange error problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 21st 2010, 05:59 PM
  3. Replies: 0
    Last Post: May 30th 2009, 08:50 PM
  4. Lagrange Error
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 29th 2009, 04:51 PM
  5. Lagrange Error and Approximating Value Help
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 6th 2008, 04:10 PM

Search Tags


/mathhelpforum @mathhelpforum