Results 1 to 2 of 2

Math Help - Taylor's series

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    62

    Taylor's series

    Hi, how do I find the Taylor's series around zero for this:

    f(x)=(sinh^3(X))/(X^5+2 X^3)

    because
    f(0)=0/0
    f'(0)=0/0

    etc



    thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    First You can verify the 'identity'...

    \displaystyle f(x)= \frac{\sinh^{3} x}{x^{5}+2 x^{3}} = \frac{1}{2}\ \frac{1}{1+\frac{x^{2}}{2}}\ \frac{\sinh^{3} x}{x^{3}} (1)

    ... and the observe that is...

    \displaystyle  \frac{1}{2}\ \frac{1}{1+\frac{x^{2}}{2}} = \frac{1}{2}\ \sum_{n=0}^{\infty} (-1)^{n}\ (\frac{x^{2}}{2})^{n} (2)

    \displaystyle \frac{\sinh x}{x} = \sum_{n=0}^{\infty} \frac{x^{2n}}{(2n+1)!} (3)

    ... so that You have all the elements to compute all the derivatioves of f(*) in 0...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Getting stuck on series - can't develop Taylor series.
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: October 5th 2010, 08:32 AM
  2. Replies: 0
    Last Post: January 26th 2010, 08:06 AM
  3. Formal power series & Taylor series
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: April 19th 2009, 09:01 AM
  4. Taylor Series / Power Series
    Posted in the Calculus Forum
    Replies: 6
    Last Post: March 4th 2009, 01:56 PM
  5. Replies: 9
    Last Post: April 3rd 2008, 05:50 PM

Search Tags


/mathhelpforum @mathhelpforum