Results 1 to 3 of 3

Math Help - Maclaurin series problem

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    10

    Maclaurin series problem

    Hi I need help with this problem...

    Construct the first three nonzero terms and the general term of the Maclaurin series generated by the function and give the interval of convergence:

    cos(x+2)

    In a page of my textbook it gives the general Maclaurin series for just cos(x) but when I ask my teacher whether it's just simply plugging in the (x+2), she says it's not. The question also gives the hint that cos(x+2) = (cos2)(cosx)-(sin2)(sinx) but I am not sure what you can do with this hint?
    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
    For the function...

    f(x)= \cos (x+2)

    ... is...

    f(0)= \cos 2

    f^{'}(0)= -\sin 2

    f^{(2} (0) = - \cos 2

    f^{(3)} (0) = \sin 2

    \dots

    ... so that the McLaurin expansion is...

    \cos (x+2) = \cos 2\cdot (1-\frac{x^{2}}{2!} + \frac{x^{4}}{4!} - \dots) + \sin 2\cdot  (-x + \frac{x^{3}}{3!} - \frac{x^{5}}{5!} + \dots)

    ... and the series converges for any real or even complex x...

    Kind regards

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

  3. #3
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    cos(2)cos(x) = cos(2)(1 - x^2/2+......

    sin(2)sin(x) = sin(2)(x +........

    this should help now add them

    or you could generate from scratch:

    f(0) = cos(2)

    f ' (0) = -sin(2)

    f " (0) = -cos(2)

    f(x) -> cos(2) -sin(2)x -cos(2)x^2/2

    For the general term see attachment--for each k there are 2 terms
    Attached Thumbnails Attached Thumbnails Maclaurin series problem-macclaurin.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. question on confusing maclaurin series problem
    Posted in the Calculus Forum
    Replies: 5
    Last Post: August 17th 2010, 08:29 AM
  2. maclaurin series problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 8th 2010, 05:18 PM
  3. Maclaurin Series Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 27th 2009, 10:30 PM
  4. MacLAurin Series problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 27th 2009, 12:10 AM
  5. Maclaurin Series Problem
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 20th 2008, 06:36 PM

Search Tags


/mathhelpforum @mathhelpforum