当x趋向于0,求1/sin^2-1/x^2的极限.洛必达求导不来.

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当x趋向于0,求1/sin^2-1/x^2的极限.洛必达求导不来.当x趋向于0,求1/sin^2-1/x^2的极限.洛必达求导不来.当x趋向于0,求1/sin^2-1/x^2的极限.洛必达求导不来.l

当x趋向于0,求1/sin^2-1/x^2的极限.洛必达求导不来.
当x趋向于0,求1/sin^2-1/x^2的极限.洛必达求导不来.

当x趋向于0,求1/sin^2-1/x^2的极限.洛必达求导不来.
lim(1/sin^2x-1/x^2)
=lim(x^2-sin^2x)/(x^2sin^2x)
=lim(x^2-sin^2x)/(x^4)
=lim(2x-sin2x)/4x^3
=lim(2-2cos2x)/12x^2
=lim4sin2x/24x
=1/3

lim(1/sin^2x-1/x^2)
=lim(x^2-sin^2x)/(x^2sin^2x)
=lim(x^2-sin^2x)/(x^4)
=lim(2x-sin2x)/4x^3
=lim(2-2cos2x)/12x^2
=lim4sin2x/24x
=1/3