求极限 lim(sin2x/sin3x)x->0x→0

分类: 作业答案 • 2021-12-18 21:39:28

问题描述：

求极限 lim(sin2x/sin3x)
x->0
x→0

答

lim(sin2x/sin3x)
=lim(xsin2x/xsin3x)
=lim2/3(3xsin2x/2xsin3x)
=lim2/3(sin2x/2x)/(sin3x/3x)
=2/3lim(sin2x/2x)/lim(sin3x/3x)
=2/3