lim(x→无穷)x^(1/x)
=lim(x→无穷)e^[lnx/x]
所以求出lim(x→无穷)lnx/x
=lim(x→无穷)(1/x)/1
=0
所以lim(x→无穷)x^(1/x)=e^0=1