[lin(1/x)]^xx趋向于0

Question

[lin(1/x)]^x x趋向于0

Answer 1

x趋向于0
lim (1/x)]^x =lim e^{xln(1/x)}= e^{limxln(1/x)}=e^{limln(1/x)/(1/x)}
u=1/x x→0,u→∞
limln(1/x)/(1/x)=lim {lnu}/u=lim {1/u}/1=0
lim (1/x)]^x =e^0=1