原式=e^lim(x->π/2)sin2xlntanx
=e^lim(x->π/2)(lntanx)/csc2x
=e^lim(x->π/2)[(1/tanx)·sec方x]/(-2csc2xcot2x)
=e^lim(x->π/2)[(-2sin方2x/(cos2xsinxcosx)]
=e^lim(x->π/2)[(-4sin方2x/(cos2xsin2x)]
=e^lim(x->π/2)[(-4sin2x/(cos2x)]
=e^0
=1
原式=e^lim(x->π/2)sin2xlntanx
=e^lim(x->π/2)(lntanx)/csc2x
=e^lim(x->π/2)[(1/tanx)·sec方x]/(-2csc2xcot2x)
=e^lim(x->π/2)[(-2sin方2x/(cos2xsinxcosx)]
=e^lim(x->π/2)[(-4sin方2x/(cos2xsin2x)]
=e^lim(x->π/2)[(-4sin2x/(cos2x)]
=e^0
=1