lim（x→0）[（sinx）^2-x^2（cosx）^2]/[x（e^2x-1）ln[1+（tanx）^2]]
=lim（x→0）[（sinx）^2-x^2（cosx）^2]/[x*2x*（tanx）^2]
=lim（x→0）[（sinx）^2-x^2（cosx）^2]/[x*2x*x^2]
=lim（x→0）[（sinx）^2-x^2（cosx）^2]/[2x^4](0/0)
=lim（x→0）[2sinxcosx-2x（cosx）^2+2x^2sinxcosx]/(8x^3)
=lim（x→0）cosx[2sinx-2x（cosx）+2x^2sinx]/(8x^3)
=lim（x→0）[2sinx-2x（cosx）+2x^2sinx]/(8x^3)
=lim（x→0）(2sinx-2xcosx+2x^2sinx)/(8x^3)(0/0)
=lim（x→0）(2cosx-2cosx+2xsinx+4xsinx+2x^2cosx)/(24x^2)
=lim（x→0）(6xsinx+2x^2cosx)/(24x^2)
=lim（x→0）2x(3sinx+xcosx)/(24x^2)
=lim（x→0）(3sinx+xcosx)/(12x) (0/0)
=lim（x→0）(3cosx+cosx-xsinx)/12
=4/12
=1/3