Results 1 to 4 of 4

Math Help - Error in Taylor Polynomial

  1. #1
    Junior Member
    Joined
    Jun 2008
    Posts
    53

    Error in Taylor Polynomial

    Completely lost, all help appreciated


    1) Bound the error in the approximation

    sin(x) ≈ x

    for -pi/4 ≤ x ≤ pi/4

    --------------------------------------

    Let p(x) be the Taylor polynomial of degree n of the function
    f(x) = log(1-x) about a = 0.

    How large should n be to have

    | f(x)-p(x) | ≤ 10^(-4) for -1/2 ≤ x ≤ 1/2 ?


    For -1 ≤ x ≤ 1/2
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    \sin(x)\;=\;x - \frac{1}{6}x^{3} + OtherStuff

    The alternating sign of the terms is VERY helpful.

    What is the size of the first term omitted on the desired interval?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jun 2008
    Posts
    53
    The error is less than the first term not used in the approximation

    |-x^3/3!| < pi^3/(4^3*3)= pi^3/384.

    So is that the answer??

    If they ask, "What is the taylor polynomial of degree 3?"

    Do you make sure that you have x^3 and no higher degree? Or do you keep 3 terms or? How do you know what's degree 3, etc. Thanks.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Aug 2007
    From
    USA
    Posts
    3,110
    Thanks
    2
    Quote Originally Posted by amor_vincit_omnia View Post
    The error is less than the first term not used in the approximation

    |-x^3/3!| < pi^3/(4^3*3)= pi^3/384.
    That's the idea, but are you sure that's where the maximum value occurs, AT \frac{\pi}{4}? Also, 3! = 6, not 3. 3! = 3*2*1

    If they ask, "What is the taylor polynomial of degree 3?"
    Quit when you have a term in x^3 or of higher degree. For example, I dare you to find a degree 3 polynomial for f(x) = cos(x). Please don't count the number of terms while looking for degree.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Error in taylor polynomial
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 18th 2010, 10:27 PM
  2. taylor polynomial error
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 16th 2009, 11:00 PM
  3. Taylor Polynomial Error
    Posted in the Calculus Forum
    Replies: 16
    Last Post: May 10th 2009, 11:58 AM
  4. error bound taylor polynomial
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 3rd 2009, 12:35 AM
  5. Taylor Polynomial (Approximation Error)
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 18th 2008, 07:38 PM

Search Tags


/mathhelpforum @mathhelpforum