# Limit problem

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1. Nov 10, 2014

### glmrkl

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. Nov 10, 2014

### RUber

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

3. Nov 10, 2014

### RUber

If you have not seen the exponential derivative before, it just requires a few steps:
$\frac{d}{dn} 2^n =\frac{d}{dn} e^{\ln 2^n}=\frac{d}{dn} e^{n\ln 2}=e^{n\ln 2}\ln 2=2^n \ln 2$

4. Nov 10, 2014

### glmrkl

Thanks a lot!

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