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如图,A,B是函数y=a x (a>1)在y轴右侧图象上的两点,分别过A,B作y轴的垂线与y轴交于E,F两点,与函数y=e x 的图象交于C,D两点,且A是CE的中点. (Ⅰ)求a的值; (Ⅱ)当直线BC与y轴平行时,设B点的横坐标为x,四边形ABDC的面积为f(x),求f(x)的解析式; (Ⅲ)若对任意的正数b,关于x的不等式 2f(x) e x -1 < 3e x ln x b e m 在区间[1,e]上恒成立,求实数m的取值范围.
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