lim(x →0)sin3x/tan2x

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lim(x →0)sin3x/tan2x
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lim(x →0)sin3x/tan2x
lim(x →0)sin3x/tan2x

lim(x →0)sin3x/tan2x
x →0
则sin3x/3x和tan2x/2x极限都是1
所以原式=lim(x →0)(3/2)*(sin3x/3x)/(tan2x/2x)
=3/2

分子求导将零代入等于3,分母求导将零代入等于2所以极限为3/2(根据导数定义推导,转化成求导数)