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在研究利用导数证明不等式时,利用一个重要的对数不等式ln(1+x)≤x(x>-1),可以证明一些不等式,达到事半功倍的效果.一、对数不等式ln(1+x)≤x(x>-1)的证明求证:ln(1+x)≤x(x>-1).证明构造函数f(x)=ln(1+x)-x,
In the study of using derivatives to prove inequalities, we can prove some inequalities by using an important logarithmic inequality ln (1 + x) ≤x (x> -1) ) ≤x (x> -1): ln (1 + x) ≤x (x> -1). Proof Constructor f (x) = ln (1 + x) -x,