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 Serie

  1. Feb 20, 2008 #1
    Let us take the first three non-zero terms of Maclaurin's expansion of
    f(x)= Asen(ax) + Bcos(ax).
    Determine for which values of a the equation f ' '(x) + f(x) = 0.
  2. jcsd
  3. Feb 21, 2008 #2

    Gib Z

    User Avatar
    Homework Helper

    Welcome to Physicsforums Oswald.

    In this case it seems better to leave f(x) in exact form. Can you find f''(x) and express it in terms of f(x) ?
  4. Feb 21, 2008 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    That looks like a homework problem and you haven't said anything about what YOU have already done. Do you know how to find the MacLaurin's series for a function?
  5. Feb 21, 2008 #4
    Maclaurin Serie solution

    I have done this, but it doesn't work...
    A sin(ax) = A[ ∑ (-1)^k . (ax)^2k+1 ] / (2k+1)! to find Maclaurin series of A sin(ax)
    B cos(ax) = B[ ∑ (-1)^k . (ax)^2k ] / (2k)! is Maclaurin Series of B cos(ax)


    A sin(ax) = Aax - Aa³x³/6 + Aa^5x^5/120

    B cos(ax) = 1 - Ba²x²/2 + Ba^4x^4/24

    f''(x) + f(x) = 0

    what is f''(x)? I think its:

    f''(x) = 0 + 1
    f(x) = A sen(ax) + B cos(ax)


    0 + 1 + Asen(ax) + B cos(ax) = 0

    Asen(ax) + Bcos(ax) = -1

    the answer is a= 1 and a= -1, but i dont know how. Is the value of A, B and x important?
    Last edited: Feb 21, 2008
  6. Feb 21, 2008 #5
    Hi,i found the solution in yahoo...

    Take your function and differentiate it twice. observe that

    f '' (x) = - a^2 f(x)

    Substitute this into the equation. One possibility is that
    A=B=0. Otherwise, cancel f(x) and you have a simple algebraic equation for a to solve.
    have done:
    f²(x)= -a²f(x)
    a= 1 or -1!
    i don't know why the teacher ask for Maclaurin series...
  7. Feb 22, 2008 #6

    Gib Z

    User Avatar
    Homework Helper

    I don't know why you didn't just take my hint, which got at exactly the same thing, rather than go to Yahoo.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Maclaurin Serie
  1. Maclaurin Series (Replies: 6)

  2. Maclaurin formula (Replies: 2)

  3. Summing a series (Replies: 1)

  4. Series question (Replies: 2)