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Limit problem, please help!

  1. Apr 19, 2008 #1

    I've been given a long limit problem to solve and i got stuck on this part in the question. Could someone please give me hints or suggestions on where to go next?

    Given that [tex]\frac{e^{x}}{x^{n}}[/tex] > e[tex]^{x - n\sqrt{x}}[/tex]

    Find the [tex]lim_{x\rightarrow+\infty}[/tex] [tex]\frac{e^{x}}{x^{n}}[/tex]

    Well i know that [tex]lim_{x\rightarrow\infty}[/tex] e[tex]^{x}[/tex] = [tex]\infty[/tex]

    but i think the question would like us to use the inequality above.

    Any help would be greatly appreciated :)
  2. jcsd
  3. Apr 19, 2008 #2

    Tom Mattson

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    I don't see how the inequality helps. Do you know about power series? If so, then can you write down a power series for the function [itex]e^x/x^n[/itex], and take its limit?
  4. Apr 19, 2008 #3
    umm... i haven't learnt power series... Is there another approach i could take??
    i tried l'hospitals rule but my answer didn't help much in this...
  5. Apr 19, 2008 #4


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    Hi caelestis! :smile:

    Hint: prove that lim (x - n√x) = ∞. :smile:
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