Hi, can someone show me how to find this limit i cant figure it out. Lim as k goes to infinity (k^(1/k))/5 ?

Thank you

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- May 18th 2008, 05:35 PMcowboys111help finding a limit
Hi, can someone show me how to find this limit i cant figure it out. Lim as k goes to infinity (k^(1/k))/5 ?

Thank you - May 18th 2008, 05:41 PMicemanfan
- May 18th 2008, 05:48 PMMathstud28
$\displaystyle L=\lim_{k\to\infty}\frac{\sqrt[k]{k}}{5}$

Taking the natural log of both sides gives

$\displaystyle \ln(L)=\lim_{k\to\infty}\frac{\ln(k)}{k}-\ln(5)$

Since this yields an indeterminate form we apply L'hopitals rule go get

$\displaystyle \ln(L)=\lim_{k\to\infty}\frac{\frac{1}{k}}{1}-\ln(5)=-\ln(5)$

So $\displaystyle L=e^{-\ln(5)}=\frac{1}{5}$ - May 18th 2008, 06:12 PMMathstud28
- May 18th 2008, 06:18 PMcowboys111
thank you