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Can someone tell me where I'm wrong with the taylor series?

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    hi guys

    I want to get taylor series of this function:


    now considering taylor expansion by den. and num. only we have:

    2 x^2-(4 x^4)/3+O(x^6)............ / x^2-(x^4/2)+O(x^6)..........

    as you see, running a simple polynomial division, eliminates all x variables so in the end there'd be only numbers coming out. which shouldn't be the case...can you see where I'm wrong? thanks
  2. Offline

    How does polynomial long division eliminate all the x variables? The coefficients are different, so that's impossible.

    Assuming your Taylor expansions for x\sin 2x and \ln (1+x^2) are correct, what you should do is write it as

    \left( 2x^2 - \dfrac{4}{3} x^4 + O(x^6) \right) \left( x^2 - \dfrac{1}{2}x^4 + O(x^6) \right)^{-1}

    and then use some kind of binomial-ish expansion on the second bracket.
  3. Offline

    that some kind of binomial-ish expansion on the second bracket is what I was asking....

    edit: got the answer!! ok thanks


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Updated: May 5, 2012
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