Question

find the limit
(1-e^x)^(2/x)
Limit as x approaches 0

Answer 1

To find L=Lim (1-e^x)^(2/x) as x->0
Take log:
L'=lim (2/x)*log(1-e^x) as x->0
=lim 2log(1-e^x)/x Apply de l'hôpital's rule
=lim -2e^x/(1-e^x)*1 as x->0
=inf
=>
L=e^L'=inf