Lim1/x arccotx ,x趋向无穷,求极限?

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Lim1/x arccotx ,x趋向无穷,求极限?

Lim1/x arccotx ,x趋向无穷,求极限?
Lim1/x arccotx ,x趋向无穷,求极限?

Lim1/x arccotx ,x趋向无穷,求极限?
令t=1/x,则arccotx =arccot(1/t)=arctan t
x趋向无穷则t趋向0,
则原式=Lim t / arctan t ,t趋向0
=Lim t / t
=1