Results 1 to 4 of 4

Math Help - taylor polynomials question

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    249

    taylor polynomials question

    For what values of x is the approximate formula: ln(1 + x) = x - (1/2)(x^2) correct to 3 decimal places?

    so i know that this is basically the maclaurin series representation of ln(1 + x) since a = 0. i used the convergence test for alternating series and confirmed that this series is indeed converging. so therefore i use the formula for the remainder which is Rn < |a_(n+1)|.

    so the first term of the series omited is (1/3)x^3, so |x^3| / 3 should be less than .001 right? since you want the error to be within 3 decimal places. but in my book, they did |x^3| / 3 < .0005. how did they get that?
    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 oblixps View Post
    For what values of x is the approximate formula: ln(1 + x) = x - (1/2)(x^2) correct to 3 decimal places?

    so i know that this is basically the maclaurin series representation of ln(1 + x) since a = 0. i used the convergence test for alternating series and confirmed that this series is indeed converging. so therefore i use the formula for the remainder which is Rn < |a_(n+1)|.

    so the first term of the series omited is (1/3)x^3, so |x^3| / 3 should be less than .001 right? since you want the error to be within 3 decimal places. but in my book, they did |x^3| / 3 < .0005. how did they get that?
    1.0006 to three decimal place is 1.001 but the error is 0.0004

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Aug 2008
    Posts
    249
    Quote Originally Posted by CaptainBlack View Post
    1.0006 to three decimal place is 1.001 but the error is 0.0004

    CB
    no you didn't answer my question. besides the question in my book isn't asking for the error. my question was:

    the first omitted term is (1/3)x^3, so |x^3| / 3 should be less than .001 right? since you want the error to be within 3 decimal places.

    but in my book, they did |x^3| / 3 < .0005. how did they get that?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member alunw's Avatar
    Joined
    May 2009
    Posts
    188
    I think Captain Black already answered your question. If you want an answer to be surely correct to 3 decimal places the maximum error has to be no more than half of 0.001 i.e. 0.0005 and not 0.001. If you use any larger value the answer will sometimes be correct but sometimes the last digit will be wrong by 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Taylor Polynomials
    Posted in the Calculus Forum
    Replies: 4
    Last Post: August 11th 2010, 03:03 PM
  2. Taylor polynomials
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 2nd 2010, 12:32 PM
  3. question on taylor polynomials
    Posted in the Calculus Forum
    Replies: 5
    Last Post: July 23rd 2009, 10:48 PM
  4. Taylor polynomials question
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 10th 2008, 05:32 PM
  5. 1 Last Question on Taylor Polynomials
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 5th 2008, 08:36 PM

Search Tags


/mathhelpforum @mathhelpforum