1 . 已知函数
.
(1)判断
的奇偶性;
(2)若
,判断
在
的单调性,并证明(定义法、导数法均可);
(3)若
,
,判断函数
的零点个数,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaf6edebbf204ca0e7462d7ece59fca1.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d013331d969749c306909529a88a49.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada9b792b1555668175c590447b02fb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次
名校
2 . 已知函数
,
.
(1)若
,
恒成立,求实数
的取值范围;
(2)证明关于
的方程
有唯一的实数根;
(3)若函数
在区间
内恰有一个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d594aae8b7ee78806af526ab1cc3d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7a129587e063a30e6d6449637f2b19.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-01-04更新
|
270次组卷
|
2卷引用:天津市宁河区芦台第一中学2021-2022学年高一上学期第二次阶段性检测数学试题
2018高三·江苏·专题练习
名校
3 . 已知函数
.
(Ⅰ)若
,求函数
在
上的零点个数(
为自然对数的底数);
(Ⅱ)若
恰有一个零点,求
的取值集合;
(Ⅲ)若
有两零点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45e2e0dc3d3bfbd29126cdeb4ef1adca.png)
(Ⅰ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b1b825dd45b1031f9cd964c575e573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅲ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0cd9f84cccef7080374fb634a1d9ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7708bda4301cb62d84a94c49d02b8f.png)
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