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
答
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