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Thread: Taylor series help

  1. #1
    jut is offline
    Junior Member
    Jul 2007

    Taylor series help [never mind solved it myself]

    In the Taylor series

    $\displaystyle u(x+h)=u(x)+hu'(x)+\frac{1}{2}h^2 u''(x)+\frac{1}{6}h^3 u'''(x)+...$

    find the number a in the next term $\displaystyle a h^4 u''''(x)$ by testing $\displaystyle u(x)=x^4$ at x=0

    OK, so, I take the 4th derivative of u(x): u''''(x)=24 and u''''(4)=24

    Now I have $\displaystyle a h^4 24$ as my next term, but how does that help me find the constant a? I'm confused.

    Ah, wait a minute, I see it.

    $\displaystyle u(x+h)=(x+h)^4=h^4+4 h^3 x+6 h^2 x^2+4 h x^3+x^4$

    The $\displaystyle h^4$ term has a coefficient of 1. So $\displaystyle 1=a 24$ and $\displaystyle a=\frac{1}{24}$

    Last edited by jut; Oct 1st 2009 at 01:02 AM.
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