证明:当x >0时,arctan x+1/x>π/2

问题描述:

证明:当x >0时,arctan x+1/x>π/2

f'(x)=1/(1+x^2)-1/x^2=-1/(1+x^2)x^2f(x)在x>0上单调递减
lim(x趋近于正无穷)f(x)=π/2+0=π/2
∴arctan x+1/x>π/2