证明不等式:当x>0时,ln(1+x)>x-x2/2
问题描述：
证明不等式:当x>0时,ln(1+x)>x-x2/2
答
f(x)=ln(x+1)-x+x^2/2f'=1/(x+1)-1+x=(x^2+x-x-1+1)/(x+1)=(x^2)/(x+1)当x>0时,f'=(x^2)/(x+1)>0f(x)=ln(x+1)-x+x^2/2递增f(x)>f(0)=0即：ln(x+1)-x+x^2/2>0ln(1+x)>x-x2/2