证明：构造函数f(x)=arctanx-x/(x+1),f(x)在(0,+∞)内连续可导f'(x)=1/(1+x²)-1/(x+1)²∵x>0∴(x+1)²=1+x²+2x>1+x²>0∴1/(1+x²)>1/(x+1)²∴f'(x)>0,f(x)在(0,+∞)内单调递增∴f(...