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Help expansion

  1. Jun 2, 2006 #1
    help!!! expansion

    hi, I am trying to expand a function and can't seem to do it, if some one can tell me how to do it i would appreciate it trmendously. The following is the function;

    f(x)=exp(x)/(exp(x)-1)^2

    im guessing it is something simple, but i just can't grasp it.

    Thank you for your time

    newo
     
  2. jcsd
  3. Jun 2, 2006 #2

    berkeman

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    Staff: Mentor

    What do you mean by expand? Do you mean just multiplying out the denominator?

    [tex]f(x) = \frac{e^x}{e^{2x} - 2e^x + 1}[/tex]
     
  4. Jun 2, 2006 #3
    im just seing if there is a series expansion for the above, if not then it doesn't matter.
     
  5. Jun 2, 2006 #4

    arildno

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    Of course there exists a series expansion of that function, why do you ask?
     
  6. Jun 2, 2006 #5
    coz i need it, I can't find it!!!!

    by the way i have looked for it but my books are limited and im not at uni at the mo so can't go to the library.
     
  7. Jun 2, 2006 #6

    arildno

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    Well, compute the first few terms of the Taylor series about some point, then! :smile:
     
  8. Jun 2, 2006 #7
    How about adding and subtracting 1 from the numerator ?
     
  9. Jun 2, 2006 #8

    arildno

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    Well, it might be simpler to write:
    [tex]f(x)=\frac{d}{dx}\frac{1}{1-e^{x}}[/tex]
    and expand the denominator in the differentiand to the degree desired.
     
  10. Jun 4, 2006 #9
    its ok after looking through some stuff and asking my dad, lol I suddenly remembered about the taylor series of exp(x)=1+x+x^2/2! etc... and if x=c/a and if a>>c we can negate x^2 term due to being much smaller than the x term hence,

    exp(x)---> 1+x

    and I get what I needed anyway from that so thats great thanks anyway
     
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