求极限lim(x→0)(tanx-sinx)/(x-sinx)
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求极限lim(x→0)(tanx-sinx)/(x-sinx)
求极限lim(x→0)(tanx-sinx)/(x-sinx)
求极限lim(x→0)(tanx-sinx)/(x-sinx)
先用洛毕塔法则
原式= lim (sec²x-cosx)/(1-cosx)
=lim (1-cos³x)/((1-cosx)cos²x)
= lim (1-cos³x)/(1-cosx) / lim 1/cos²x
=lim (1-cosx)(1+cosx+cos²x)/(1-cosx)
=lim 1+cosx+cos²x
=3
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