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Homework Help: Taylor Series Expansion

  1. Nov 17, 2005 #1
    y=kcosh(x/k) = k(e^(x/w) + e^(-x/k))

    y ~ k[1 + x/k + (1/2!)(x^2/k^2) + (1/3!)(x^3/k^3)] +...+ k[1 - x/k +(1/2!)(x^2/k^2) - (1/3!)(x^3/k^3) +...]

    All odd terms except 1 cancel out.

    So we are left with

    y = k [2 + (2/2!)(x^2/k^2) + (2/4!)(x^4/k^4) + (2/6!)(x^6/k^6) +....]

    I've been staring at this for hours and I'm supposed to show that:

    y= k + (1/2k)(x^2) for k>>x


    What did I do wrong??? My error lies somewhere where the twos are bolded.
     
  2. jcsd
  3. Nov 17, 2005 #2

    shmoe

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    you lost a 1/2 in your definition of cosh:

    [tex]cosh(x)=\frac{e^x+e^{-x}}{2}[/tex]
     
  4. Nov 17, 2005 #3

    Hurkyl

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    Well, you obviously are missing a factor of two somewhere... but I suppose you figured that out already. The answer lies here:

    [tex]\cosh x = \frac{e^x + e^{-x}}{2}[/tex]
     
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