1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Maclaurin series coefficient

  1. Apr 16, 2009 #1
    1. The problem statement, all variables and given/known data
    find coefficient of x^4 in the MAclaurin series for f(x)=e^sinx


    2. Relevant equations
    ok... so taking derivatives 4 times for this function.....gave me a mess!!! @.@
    can someone help me in simplying the derivatives...?
    1. cosxe^sinx
    then for 2. is it -sinxe^sinx-sinxcosxe^sinx....?
    = . = i'm getting lost with these derivatives.....

    same for e^3xcos2x... gets sooo complicated...
     
    Last edited: Apr 16, 2009
  2. jcsd
  3. Apr 16, 2009 #2
    Don't try to find it by determining the derivatives. You already know the expansions of the function sin x and e^y. Just plug them in, and expand up till 4th order (or better to just look what terms contribute to the x^4 coefficient).

    E.g.:
    [tex]e^{\sin x} = \sum_{k=0}^\infty \frac{(\sin x)^k}{k!}[/tex]

    Then plug in the expansion for sin x and collect the terms.
     
  4. Apr 17, 2009 #3
    hmm i'm still not too sure...
    I do get the series u've written above... now for sinx i expand it like x - x^3/3! + x^5/5!... up to the fourth order.... and plug in 0??.... doesn't that just make everything equal to 0.....????
     
  5. Apr 18, 2009 #4

    Mark44

    Staff: Mentor

    I think what xepma is talking about is this[tex]e^{\sin x} = \sum_{k=0}^\infty \frac{(\sin x)^k}{k!}[/tex]
    [tex]= 1 + sin(x)/1 + sin^2(x)/2 + sin^3(x)/3! + ...[/tex]

    Now, put in your series for sin(x), sin2(x) and so on. You probably won't need the sin3(x) and might need only a term or two for the sin2(x) part.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Maclaurin series coefficient
  1. Maclaurin series (Replies: 5)

  2. Maclaurin series (Replies: 2)

  3. Maclaurin Series (Replies: 3)

  4. Maclaurin series (Replies: 8)

Loading...