用等价无穷小代换:tanx-sinx~(x^3)/2
lim x→0 3x^3/tanx
= lim x→0 (3/2) ( tanx - sinx )/tanx
= (3/2) lim x→0 ( 1 - sinx/tanx )
= (3/2) lim x→0 ( 1 - cosx )
= (3/2)( 1 - 1 )
= 0 。
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