1/x²-cot²x
=(1-x²cot²x)/x²
=(sin²x-x²cos²x)/(x²sin²x)
=(sin²x-x²cos²x)/x^4
0/0洛必达
=(2sinxcosx-2xcos²x+2x²sinxcosx)/(4x^3)
=[(1+x²)sin2x-2xcos²x]/(4x^3)
0/0洛必达
=[2xsin2x+(1+x²)2cos2x-2cos²x+4xsinxcosx]/(12x^2)
=[4xsin2x-2cos²x+2(1+x²)cos2x]/(12x^2)
=[4sin2x+8xcos2x+4sinxcosx+4xcos2x-4(1+x^2)sin2x]/(24x)
=[(2-4x^2)sin2x+12xcos2x]/(24x)
0/0洛必达
=[-8xsin2x+2(2-4x^2)cos2x+12cos2x-24xsin2x]/24
=16/24
=2/3