题目内容
(14分)己知函数f (x)=ex,x
R
(1)求 f (x)的反函数图象上点(1,0)处的切线方程。
(2)证明:曲线y=f(x)与曲线y=
有唯一公共点;
(3)设
,比较
与
的大小,并说明理由。
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(1)求 f (x)的反函数图象上点(1,0)处的切线方程。
(2)证明:曲线y=f(x)与曲线y=
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(3)设
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(1)
;(2) 详见解析;(3) 
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.
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试题分析:(1)f (x)的反函数
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(2)曲线y=f(x)与曲线
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(3) 比较两个式子的大小的一般方法是用比较法,即作差,变形,判断符号.
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结合这个式子的特征可看出,我们可研究函数
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试题解析:(1) f (x)的反函数为
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(2) 令
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(3) 设
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令
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当
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所以当
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