以下省略x趋于0,
lim (1+2sin^2 2x)^[1/ln(1-x^2)]
=lim (1+2sin^2 2x)^{[1/2sin^2 2x]*[2sin^2 2x/ln(1-x^2)]}
=e^lim [2sin^2 2x/ln(1-x^2)]
=e^lim [2*(2x)^2/(-x^2)]
=e^(-8)