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58问答库 > lim√（1-cosx)⼀tanx用等价无穷小代换求极限

lim√（1-cosx)⼀tanx用等价无穷小代换求极限

2025-03-21 18:23:02

推荐回答（2个）

回答（1）：

lim√(1-cosx)/tanx
=lim-√2sin(x/2)/tanx
=lim-√2/2x/x
=-√2/2
lim√(1-cosx)/tanx
=lim√2sin(x/2)/tanx
=lim√2/2x/x
=√2/2
因为lim√(1-cosx)/tanx≠lim=√(1-cosx)/tanx
所以极限不存在

回答（2）：

因为第一步不能代换
只有在乘除运算中才能用等价无穷代换加减不行课本上有
比如：(1-cosx)/x
如果用代换 2sinx/2~2*x/2=x lim=1
如果用罗比达 =lim sinx/1=0

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