Results 1 to 3 of 3

Math Help - Taylors approximation problem

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    10

    Taylors approximation problem

    dx/dt = 1- sin[ ln(1+x )]

    Replace the right hand side by the linear Taylor's approximation about x0=0 and solve the resulting equation. Determine the particular solution for the initial condition x(0)=0.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,391
    Thanks
    55
    Taylor series for \ln(1+x) and \sin x

    \ln (1+x) = x - \dfrac{x^2}{2} + \dfrac{x^3}{3} \cdots
    \sin x = x - \dfrac{x^3}{3!} + \dfrac{x^5}{5!} \cdots

    so to first order the taylor series would be

    \sin (\ln(1+x)) = x
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    10
    Hadn't learnt the Taylor series so had to do a quick crash course, this helped a lot, thanks heaps.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Taylors Series Confusion
    Posted in the Calculus Forum
    Replies: 2
    Last Post: April 29th 2011, 12:14 AM
  2. Taylors Theorem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: July 19th 2010, 10:54 AM
  3. Deriving Taylors for 1/(1-X)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 13th 2009, 01:57 AM
  4. taylors theorem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 11th 2008, 03:38 AM
  5. taylors series
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 23rd 2007, 02:05 PM

Search Tags


/mathhelpforum @mathhelpforum