lim{x->0}[(1+x)/(1-x)]^(1/x)
=lim{x->0}[1+2x/(1-x)]^{[(1-x)/(2x)]*[2/(1-x)]}
=lim{x->0}{[1+2x/(1-x)]^[(1-x)/(2x)]}^[2/(1-x)]
=e^2