1 . 已知椭圆
,点
在椭圆上,如图,用
表示椭圆在点
处切线的单位向量.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/198f7b15-d256-45b8-8ad4-3cc9057793bf.png?resizew=120)
(1)设
,求
的最大值;
(2)是否存在定圆
,使得圆
的任一切线与
的交点
满足
,若存在,求出圆
方程,若不存在,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a6e483672a226118dff5a39aa28449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f4fbb5a4568dd3e4baec9f8358552b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e8744362c6e224146461b97faf9821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/198f7b15-d256-45b8-8ad4-3cc9057793bf.png?resizew=120)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75874285daf265905257368573ded035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)是否存在定圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0a21698cc2ceabd28d995692ab2bfc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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解题方法
2 . 已知函数
,直线
为曲线
的切线(
为自然对数的底数).
(1)求实数
的值;
(2)用
表示
中的最小值,设函数
,若函数
为增函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13090a9194777b2105ecc6388301f4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221ad6017a2cc31555275742abace73b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85c34922a744db6288c376087ffb423.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976706919bfd11475467dbc7e9a647da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0aea8bc07013e9cad5b459fb15119d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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2016-12-04更新
|
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6卷引用:浙江省镇海市镇海中学2017年高中数学竞赛模拟(二)试题
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3 . 已知函数
,
.
(1)证明:
,直线
都不是曲线
的切线;
(2)若
,使
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/728f2cc68f8ca8ef2faa681785798259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770538d7235d12c0117bd2824ef8cf07.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914b349342d0f91c17878d709c16ba2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fdccde9d9d4dcad15e8889b285eda0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11f827ed65d721a3341985c9f6879d92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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4 . 已知函数
,
.
(1)若
,
,求
的单调区间;
(2)若函数
是函数
的图像的切线,求
的最小值;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972efbd8ad14fb73877c222172b18e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e542fc34c94ba82d6646cac06257050.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f442c662903757d09fb284c4fc2eec10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2316563595e29fd4279845ab8afc5ba2.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e542fc34c94ba82d6646cac06257050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/972efbd8ad14fb73877c222172b18e13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee599f1b7f0bbbbe786d00b7c27eccca.png)
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3卷引用:第十四届高二试题(B卷)-“枫叶新希望杯”全国数学大赛真题解析(高中版)
13-14高三上·安徽淮南·阶段练习
5 . 若函数
图像上任意一点
满足条件
,则称函数
具有性质
下列函数中具有性质
的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b58a5e238a27d636636efe2cd947b74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7卷引用:2013年全国高中数学联赛吉林赛区预赛试题
(已下线)2013年全国高中数学联赛吉林赛区预赛试题(已下线)2014届安徽省淮南二中高三上学期第三次月考理科数学试卷(已下线)2014届吉林省长春市高中毕业班第一次调研测试理科试卷2016-2017学年河北定州中学高一周练10.16数学试卷2017届北京市西城区高三一模文科数学试卷2017届北京市西城区高三4月统一测试(一模)文数试卷(已下线)2019高考热点题型和提分秘籍 【文数】专题7 函数的图象( 题型专练)
名校
解题方法
6 . 已知函数
.
(Ⅰ)当
时,求曲线
在
处的切线方程;
(Ⅱ)设函数
,求函数
的单调区间;
(Ⅲ)若
在
(e=2.71828…)上存在一点x0,使得
成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c370eaabb30e90a2886accb77b769e2.png)
(Ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(Ⅱ)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3531c5730f86326a2efe23a0e91a6c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(Ⅲ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/507c3f497a7633fca2b431d785375624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47e734b17201fe992be7775714e9558.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b9bfb5c6f9dbc1dc0727c8afeaef19.png)
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|
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2卷引用:广西陆川县中学2016-2017学年高二下学期知识竞赛数学(理)试题