lim x→o (tanx-x)/(x-sinx)极限怎么求呀?

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lim x→o (tanx-x)/(x-sinx)极限怎么求呀?

lim x→o (tanx-x)/(x-sinx)极限怎么求呀?
lim x→o (tanx-x)/(x-sinx)极限怎么求呀?

lim x→o (tanx-x)/(x-sinx)极限怎么求呀?
原式=lim(x->0)[(sec²x-1)/(1-cosx) (0/0型极限,应用洛必达法则)
=lim(x->0)(2sec²xtanx/sinx) (0/0型极限,应用洛必达法则)
=lim(x->0)(2/cos³x)
=2