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Limit problem

  1. Nov 10, 2014 #1
    1. The problem statement, all variables and given/known data

    http://puu.sh/cKVxE/fb13f83a75.png [Broken]
    In this image, I have no idea what the math behind this problem is. What exactly is happening here?


    2. Relevant equations



    3. The attempt at a solution
    I multiplied n/10 in order to get 10000n^9 as a denominator but the ln(2) confuses me; therefore, I cannot get to the third part of the problem.
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Nov 10, 2014 #2

    RUber

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    Homework Helper

    It appears that in each step they are taking the derivative of the [edit] top and bottom with respect to n (L'Hopital's Rule).
    Taking 10 derivatives leads to the last limit, which is clearly unbounded.
     
  4. Nov 10, 2014 #3

    RUber

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    If you have not seen the exponential derivative before, it just requires a few steps:
    ##\frac{d}{dn} 2^n =\frac{d}{dn} e^{\ln 2^n}=\frac{d}{dn} e^{n\ln 2}=e^{n\ln 2}\ln 2=2^n \ln 2 ##
     
  5. Nov 10, 2014 #4
    Thanks a lot!
     
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