求极限Lim :(ln(1+1/x))/arccotx x取正无穷大,我怎么求都是0,课本答案是1求极限Lim :(ln(1+1/x))/arccotxx取正无穷大,我怎么求都是0,

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求极限Lim:(ln(1+1/x))/arccotxx取正无穷大,我怎么求都是0,课本答案是1求极限Lim:(ln(1+1/x))/arccotxx取正无穷大,我怎么求都是0,求极限Lim:(ln(1

求极限Lim :(ln(1+1/x))/arccotx x取正无穷大,我怎么求都是0,课本答案是1求极限Lim :(ln(1+1/x))/arccotxx取正无穷大,我怎么求都是0,
求极限Lim :(ln(1+1/x))/arccotx x取正无穷大,我怎么求都是0,课本答案是1
求极限Lim :(ln(1+1/x))/arccotx
x取正无穷大,我怎么求都是0,

求极限Lim :(ln(1+1/x))/arccotx x取正无穷大,我怎么求都是0,课本答案是1求极限Lim :(ln(1+1/x))/arccotxx取正无穷大,我怎么求都是0,

arccotx=arctan1/x,
令t=1/x,则t→0,
——》原式=limt→0 ln(1+t)/arctant,
=limt→0 t/t,(ln(1+t)~t,arctant~t,替换)
=1。