名校
1 . 函数
.
(1)若曲线
存在垂直于y轴的切线,求实数a的取值范围;
(2)设
,试探究函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ea5d467834e8559088ec8e01b30089.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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5卷引用:江苏省南通市2022-2023学年高三上学期12月调研测试数学试题
名校
2 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6b4fd7ea9ebef26c80081aece3cdb8.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2868fc8e6dc8e0b15a381649a7bd5532.png)
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4卷引用:2023届高三一轮复习联考(三)全国卷文科数学试题
3 . 试估算腰长为1,顶角为20°的等腰三角形的底边长所在的区间( )
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知指数函数
(
,且
)图象与其反函数的图象有公共点,则
的取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d76ee3b131ecd6aa1aacf7fb7b3eb15.png)
![](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/4887473a8091e1ef53a169cc9f211e3a.png)
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名校
解题方法
5 . 已知函数
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14b4dbed34a6e2f86c3260bec5ea7c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab3c2bffbba4a2869ec2c6fc0659e2b.png)
A.对于任意![]() ![]() |
B.对于任意![]() ![]() ![]() |
C.对于任意![]() ![]() ![]() |
D.存在![]() ![]() |
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2卷引用:浙江省湖州、丽水、衢州三地市2022-2023学年高三上学期11月教学质量检测数学试题
名校
解题方法
6 . 欧拉对函数的发展做出了巨大贡献,除特殊符号、概念名称的界定外,欧拉还基于初等函数研究了抽象函数的性质,例如,欧拉引入倒函数的定义:对于函数
,如果对于其定义域
中任意给定的实数
,都有
,并且
,就称函数
为倒函数.
(1)已知
,
,判断
和
是不是倒函数,并说明理由;
(2)若
是
上的倒函数,当
时,
,方程
是否有正整数解?并说明理由;
(3)若
是
上的倒函数,其函数值恒大于
,且在
上是严格增函数.记
,证明:
是
的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf26cb0612e3afd9fe70bbfa46975c51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdfaa3716ef9b13f4bdfe0b234df9932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eaeb2ab68a49074d623ffca072fed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da3153b46564e0d7c0e3e063fb209123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2b74d89854116e411c089d053df053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e2bf39bacfc020ab2ffafe341a9e7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5bc39061e1fb75d8ab1fd5c3765a514.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/781adcb4e434715fadaca92bfdd0e8a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec808ad60dbf016632ec816eaca1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5226c58ca852742dca2b380d1fd4042e.png)
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5卷引用:上海市闵行区2021-2022学年高一上学期期末数学试题
上海市闵行区2021-2022学年高一上学期期末数学试题(已下线)第02讲 常用逻辑用语 (讲+练)-2023年高考数学一轮复习讲练测(新教材新高考) 上海南汇中学2023届高三上学期期中数学试题湖南省娄底市新化县2022-2023学年高一上学期期末数学试题(已下线)第5章 函数的概念、性质及应用(基础、典型、易错、压轴)分项训练-2022-2023学年高一数学考试满分全攻略(沪教版2020必修一)
7 . 已知方程
的所有实数根都在区间
内(其中
),则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f43df6ba1dcfb8b15ede19489881d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1a31921401badcd21fafdcdc4bc5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f65bb83b1daf4c79e6a10ec01a466425.png)
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8 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)讨论
的单调性;
(3)若
有两个零点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a69b48522797ce76f768dfedbe9ab72.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54647a4806763744bb6dde143c99fc1f.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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|
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名校
9 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a293d351e81321ec01e477e85f48ad.png)
(1)求
在
处的切线方程;
(2)求
在
上的最小值(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a293d351e81321ec01e477e85f48ad.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c6b6a11760d0724b0b60e55970e229.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b77857e15ae11fc94a5e33bfc12d26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
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3卷引用:湖北省黄冈市2022-2023学年高三上学期9月调研考试数学试题
10 . 已知函数
.
(1)若
在
上是增函数,求实数
的取值范围;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8163ef24d8945d690949e4a0a85077f8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da34ce730f711c09909d53806fe2330a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f25bcb0e6fb29e378fd3de0cd26056.png)
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