lim(1/x²-cot²x)
2个回答

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