2023·上海·模拟预测
名校
1 . 已知
.记
,其中常数m,
.
(1)证明:对任意m,
,曲线
过定点;
(2)证明:对任意s,
,
;
(3)若对一切
和一切使得
的函数
,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df569b67897be7670d10c7b7d06af16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e2696b1a336d7ab14b50d6ca80be95a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)证明:对任意m,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)证明:对任意s,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6819945aa00328aa3073e581cdfd39.png)
(3)若对一切
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed57d79c717fc8cf7ede3d9995c98359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4ff4809078ded17cd2674176342d6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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2 . 设
且
,若在平面直角坐标系xOy中,函数
与
的图像于直线l对称,则l与这两个函数图像的公共点的坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7bbb80619d6e1312fba9cd3a02c8f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947a492a80e26798f9570e190d0207a2.png)
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