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

当x趋向于0,求1/sin^2-1/x^2的极限.洛必达求导不来.

人气：337 ℃　时间：2020-05-25 21:10:45

解答

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