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