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Need some clarification on this limit

  1. Dec 16, 2005 #1
    I need some clarification on this limit:

    lim n-->infinity of (2^n)/(n^4)

    since the bottom of the function reaches infinity way faster than the top, why isnt the limit zero? my book says that it is infinity.
     
  2. jcsd
  3. Dec 16, 2005 #2

    Astronuc

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    Staff: Mentor

    I believe the numerator goes to infinity faster.

    Take n=100, the numberator is 2100 which would be 1625, while the denominator is 1004 = 108.

    I believe by applying l'Hôpital's rule, differentiate the numerator and denominator four-fold, the denominator becomes 4!, while the numerator is still factor of 2n
     
  4. Dec 16, 2005 #3

    Tide

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    Science Advisor
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    It might help to compare logarithms of the numerator and denominator.
     
  5. Dec 17, 2005 #4

    HallsofIvy

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    Because the top of the function reaches infinity way faster than the bottom!

    (Even 1.00001^n eventually increases faster than n^10000.)
     
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