Results 1 to 2 of 2

Math Help - Computer 10th derivative using Mclaurin series

  1. #1
    Member
    Joined
    Jun 2006
    Posts
    93

    Computer 10th derivative using Mclaurin series

    The problem is:

    f(x) = [cos(3x^2)-1]/(x^2) at x=0

    I know that the Mclaurin series for cos(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ....

    That is where I'm stuck, I can't remember how to use the Mclaurin series with this function
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by pakman View Post
    The problem is:

    f(x) = [cos(3x^2)-1]/(x^2) at x=0

    I know that the Mclaurin series for cos(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ....

    That is where I'm stuck, I can't remember how to use the Mclaurin series with this function
    Learn and watch.

    \cos x=1-\frac{x^2}{2!}+\frac{x^4}{4!}-...
    Thus, (composition of two analyic functions at a point is analytic),
    \cos (3x^2)=1-\frac{(3x^2)^2}{2!}+\frac{(3x^2)^4}{4!}-...
    Thus,
    \cos (3x^2)-1=-\frac{9x^4}{2!}+\frac{81x^8}{4!}-...
    When you divide by x^2, is the same as dividing term by term, thus,
    -\frac{9x^2}{2!}+\frac{81x^6}{4!}-...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the 10th derivative of y = cos(3x)
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 29th 2010, 08:52 PM
  2. Compute the 10th derivative of ...
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 17th 2010, 02:04 PM
  3. McLaurin series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 2nd 2010, 03:14 AM
  4. 10th derivative
    Posted in the Calculus Forum
    Replies: 9
    Last Post: August 21st 2009, 10:42 AM
  5. McLaurin Series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 20th 2009, 07:17 PM

Search Tags


/mathhelpforum @mathhelpforum