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Limit problem, please help!

  • Thread starter caelestis
  • Start date
  • #1
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Hello,

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 :)
 

Answers and Replies

  • #2
Tom Mattson
Staff Emeritus
Science Advisor
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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?
 
  • #3
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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?
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...
 
  • #4
tiny-tim
Science Advisor
Homework Helper
25,789
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Hi caelestis! :smile:

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

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