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
$\displaystyle L=\lim_{k\to\infty}\frac{\sqrt[k]{k}}{5}$
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 $\displaystyle L=e^{-\ln(5)}=\frac{1}{5}$