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Limiting value

  1. Feb 6, 2010 #1
    I cant get the following limit to work:

    lim(X->0) 1/(ix)*(exp(imx) - 1 ) = m

    I'm sorry for the poor notation. I tried expanding the exponential, and L'hopitals rule and combinations of these approaches, but i cant get it to work out. Any help is much appreciated!
     
  2. jcsd
  3. Feb 6, 2010 #2

    HallsofIvy

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    I assume you mean [itex]\lim_{x\fo 0}\frac{e^{imx}- 1}{ix}[/itex]. I can see no reason why L'Hopital's rule would not work:

    Both [itex]e^{imx}-1[/itex] and ix go to 0 as x goes to 0.

    [itex]\left(e^{imx}\right)'= im e^{imx}[/itex] while (ix)'= i. By L'Hopitals rule, the limit is the same as [itex]\lim_{x\to 0}\frac{im e^{imx}}{i}= m\left(\lim_{x\to 0}e^{imx}\right)= m[/itex].
     
  4. Feb 6, 2010 #3
    doh!! I differentiated the whole part instead of nominator and denominator separately..

    Thx alot
     
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