Results 1 to 2 of 2

Math Help - approximations using Taylor sries

  1. #1
    Member akhayoon's Avatar
    Joined
    Dec 2007
    From
    T.O
    Posts
    106

    approximations using Taylor sries

    I hear you could use taylor polynomials or series to approximate things like \sqrt9.04 for example or something like that...is that true and how can that be done?

    post number 100 yay!!!!
    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 akhayoon View Post
    I hear you could use taylor polynomials or series to approximate things like \sqrt9.04 for example or something like that...is that true and how can that be done?

    post number 100 yay!!!!
    The Taylor series for a function f about x can be writen:

    f(x+\varepsilon)=f(x)+\varepsilon f'(x) + \left(\frac{\varepsilon}{2}\right)^2f''(x)+ ... + \left(\frac{\varepsilon}{n!}\right)^nf^{(n)}(x)+ ...

    In your case f(x)=x^{1/2} , and so we have:

     <br />
(9.04)^{1/2} \approx (9)^{1/2}+0.04 \times (1/2) \times 9^{-1/2} - 0.04^2 \times (1/8) \times 9^{-3/2} ...<br /> <br />

    Which is pretty good even after just the first two terms

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Taylor series approximations
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 22nd 2011, 07:23 PM
  2. ti-84 approximations
    Posted in the Calculators Forum
    Replies: 1
    Last Post: December 3rd 2009, 09:29 PM
  3. taylor approximations
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 6th 2009, 11:46 PM
  4. Taylor series and error approximations
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: February 18th 2009, 08:21 AM
  5. Approximations, help wit 1 more please
    Posted in the Calculus Forum
    Replies: 4
    Last Post: December 18th 2007, 04:43 PM

Search Tags


/mathhelpforum @mathhelpforum