求證:當x>0時,不等式lnx>=1-1/x.

求證:當x>0時,不等式lnx>=1-1/x.

證明:
令f(x)=lnx+1/x-1
f'(x)=1/x-1/x^2=(x-1)/x^2
當x>=1時,f'(x)>=0,f(x)是增函數,當x