limx趋向0arctan(1/x)的极限

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limx趋向0arctan(1/x)的极限limx趋向0arctan(1/x)的极限limx趋向0arctan(1/x)的极限1/x->无穷大当x->0+(从右侧趋近于0)1/x->正无穷arctan

limx趋向0arctan(1/x)的极限
limx趋向0arctan(1/x)的极限

limx趋向0arctan(1/x)的极限
1/x->无穷大
当x->0+(从右侧趋近于0)1/x->正无穷
arctan(1/x)->Pi/2
当x->0-(从左侧趋近于0)1/x->负无穷
arctan(1/x)->-Pi/2
左右极限不相等,说明极限不存在

令arctan(1/x)=t (-π/2<=t<=π/2)
tant=1/x
x趋于0,1/x趋于无穷
则tant趋于无穷
则t=π/2或-π/2
limarctan(1/x)=limt=π/2或-π/2

x→0+时,1/x→+∞,arctan(1/x)→π/2
x→0-时,1/x→-∞,arctan(1/x)→-π/2
所以,x→0时,arctan(1/x)无极限