Question

lim as x approaches infinity of (ln(x)^(1/x) .

Answer 1

use lapitale rule

Answer 2

http://en.wikipedia.org/wiki/L'H%C3%B4pital's_rule
ln(x)^(1/x) = e^(1/x*ln(ln(x)))

So lim (ln(ln(x))/x) = 0 Becose (1/lnx*1/x)/1 -> 0 as x ->infty