极限的.计算limx→正无穷[x arctanx-(π/2)x]

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极限的.计算limx→正无穷[x arctanx-(π/2)x]

极限的.计算limx→正无穷[x arctanx-(π/2)x]
极限的.计算limx→正无穷[x arctanx-(π/2)x]

极限的.计算limx→正无穷[x arctanx-(π/2)x]
lim(x-> ∞) [xarctanx-(π/2)x]
=lim(x-> ∞) [arctanx -π/2] /(1/x) (0/0)
=lim(x-> ∞) [1/(1+x^2)] /(-1/x^2)
=0

lim(x→+∞)[x arctanx-(π/2)x]
=lim(x→+∞)-(xarccotx)
=lim(x→+∞)-(arccotx)/(1/x)
=lim(x→+∞)-[-1/(1+x^2)]/(-1/x^2)
=-1