let
y =1/x
lim(x->+∞) ( 1- 1/x^2)^x
=lim(y->0+) ( 1- y^2 )^(1/y)
=lim(y->0+) e^[ln( 1- y^2 )/y ]
=lim(y->0+) e^[ (-y^2 +o(y^2))/y ]
=lim(y->0+) e^[-y+o(y)]
=e^0
=1
lim(x->+∞) ( 1- 1/x)^(1-x)
=lim(x->+∞) ( 1- 1/x)^(-x)
=e
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