对于这个题,最好的方法就是数形结合,你画Y=AX,Y=LNX的图,FX实际上表示它们之间再竖方向上的距离,根据情况,你可以判定出A是正数.因为X不能等于0,实际上是求右极限等于2.于是得到关系式,LIM X+ 0(AX-LNX)=2,解得A=E.第二问还是根据数新结合,它实际上要证它是各向下凸的函数,就是俩端点的平均值高于中间值的俩倍,这本来可以用高等数学轻易解答的,因为是高三的,就用做差法就可以了.AX1-LNX1+AX2-LNX2-2A(X1+X2)/2+2LN(X1+X2)/2=-(LNX1+LNX2)+2LN(X1+X2)/2=-LNX1X2+LN(X1+X2)^2/2=LN(X1+X2)^2/2X1X2>LN1=0.
高三数学challenging math problem
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