题根(导数)
New University Entrance Examination（2016）
Abstract
题 (1)试比较32×43×54×…×2 0122011与23×34×45×…×2 011 2012的大小;
(2)已知函数f(x)在(0,+∞)上恒有xf'(x)＞f(x)成立,求证:当x1＞0,x2＞0时,f(x1) +f(x2)＜f(x1+x2);
(3)若存在两个正实数x,y,使得等式x+a(y-2ex)(lny-lnx)=0成立,其中e为自然对数的底数,求实数a的取值范围.
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