1 . 已知函数
,
(其中e为自然对数的底数,m、n为常数),函数
定义为:对每一个给定的实数x,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef35cb578663cc6bb1c55a2fc0c1807.png)
(1)当m、n满足什么条件时,
对所有的实数x恒成立;
(2)设a、b是两个实数,满足
且m,
当
时,求函数
在区间
的上的单调增区间的长度之和(用含a、b的式子表示)(闭区间
的长度定义为
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4a728265d90805da586efc106b998d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8bcd81728beee5e63192eccb05fff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef35cb578663cc6bb1c55a2fc0c1807.png)
(1)当m、n满足什么条件时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
(2)设a、b是两个实数,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0db10041e9c1f63aa25348f1f142717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba934874cc9f2ab272fdff67ea23bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be35b4d8f52e8f440297683c3178e22e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701fce58a3087d253fd4fa948030eb50.png)
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2020-02-18更新
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536次组卷
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2卷引用:湖北省武汉市华中师大一附中2018-2019学年高一上学期期末数学试题