求极限题目lim(x->+∞)arctan(x-cosxlnx)=?跪谢!

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求极限题目lim(x->+∞)arctan(x-cosxlnx)=?跪谢!求极限题目lim(x->+∞)arctan(x-cosxlnx)=?跪谢!求极限题目lim(x->+∞)arctan(x-co

求极限题目lim(x->+∞)arctan(x-cosxlnx)=?跪谢!
求极限题目lim(x->+∞)arctan(x-cosxlnx)=?跪谢!

求极限题目lim(x->+∞)arctan(x-cosxlnx)=?跪谢!
lim(x->+∞)arctan(x-cosxlnx)
=lim(x->+∞)arctanx(1-cosx*lnx/x)
因为:limlnx/x=0,cosx为有界量,故limcosx*lnx/x=0
lim(x->+∞)arctan(x-cosxlnx)
=lim(x->+∞)arctanx(1-cosx*lnx/x)
=π/2