名校
1 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5edbbc3f9dcc564f13325250a361235.png)
(1)求曲线
在点
处的切线方程;
(2)求证:函数
的图象位于直线
的下方;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5edbbc3f9dcc564f13325250a361235.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
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2 . 已知椭圆
:
(
)的半长轴的长度与焦距相等,且过焦点且与
轴垂直的直线被椭圆截得的弦长为3.
(1)求椭圆
的方程;
(2)已知直线
:
与椭圆
交于
,
两点,过点
的直线交椭圆
于
,
两点(
在靠近
的一侧)
(ⅰ)求
的取值范围;
(ⅱ)在直线
上是否存在一定点
,使
恒成立?若存在,求出
点坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0accaaa66de4dfd9ed8257fa942c2cff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7f6a03826a5ad351c1f7ca553a6945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591ccce336af06e51e7f4887c287b80f.png)
(ⅱ)在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d14da8892d33751940b69a790bc5c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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名校
解题方法
3 . 已知函数
,
.(注:
是自然对数的底数)
(1)若
无极值点,求实数
的取值范围;
(2)当
时,
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c33ef652f63f1b43282aedbf71311e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f7f23e7f20dd8bc65a4967cd306782.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797bbd18359c9a29842b39109b3a0aac.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a01be1031ca8543348a8dddc833db2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
4 . 设点
(
)是抛物线
上任意一点,过点
作抛物线
的两条切线,分别交抛物线
于点
和点
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b8e0e181de2dfa47561cc534287eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c16dac1e9bf5804c8907cbc59014d04.png)
A.![]() | B.![]() |
C.![]() | D.直线![]() ![]() |
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解题方法
5 . 设双曲线
:
(
,
)的右焦点为
,过
作双曲线的一条渐近线的垂线,垂足为
,若
(
为坐标原点),则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2a01b89c8982495257685e7b2f2930d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.3 | C.2 | D.![]() |
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名校
6 . 设
,则
的大小关系是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63cdb37f8009be5a10586fea811c6575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
7 . 已知函数
.
(1)当
时,求
在
处的切线方程;
(2)若函数
在
上单调递增,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662704fdd021f1cc3c239cb0362b4017.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)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
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名校
8 . 已知
分别满足下列关系:
,则
的大小关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c034fe93ffb4be7bec50b0c129595a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d10449bc77d692a7270e0f20a68cdf2.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 函数
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1eb4ffe8a0444b50e3d08aedfa790ae.png)
A.是偶函数,且在区间![]() | B.是偶函数,且在区间![]() |
C.是奇函数,且在区间![]() | D.既不是奇函数,也不是偶函数 |
您最近一年使用:0次
昨日更新
|
1533次组卷
|
7卷引用:湖北省武汉市华中师范大学第一附属中学2024届高三五月适应性考试数学试卷
湖北省武汉市华中师范大学第一附属中学2024届高三五月适应性考试数学试卷河北省保定市保定名校协作体2024届高三五月适应性考试(三模)数学试题广东省华南师范大学附属中学2024届高三下学期5月适应性考试数学试题湖南省长沙市长郡中学2024届高三下学期考前保温卷(二)数学试题(已下线)第三章 第二节 导数与函数的单调性【同步课时】基础卷(已下线)第02讲 导数与函数的单调性(十二大题型)(练习)-2江西省宜春市丰城中学2023-2024学年高一下学期第三次段考(5月月考)数学试题
解题方法
10 . 已知抛物线
的焦点为
,
为
上任意一点,且
的最小值为1.
(1)求抛物线
的方程;
(2)已知
为平面上一动点,且过
能向
作两条切线,切点为
,记直线
的斜率分别为
,且满足
.
①求点
的轨迹方程;
②试探究:是否存在一个圆心为
,半径为1的圆,使得过
可以作圆
的两条切线
,切线
分别交抛物线
于不同的两点
和点
,且
为定值?若存在,求圆
的方程,不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9158f21b372fd0390fab040ad65c586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/493875c56db5cf73d6417923c6cecb9d.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4099122dfb15704bb265197e1bc74e49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c30af83767217e6497d2ef64b9793b6.png)
①求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②试探究:是否存在一个圆心为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2186fca32ea8c51488e6f181fd23366e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0abef37676985bd2340ccfaae2c70192.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47d15440b1d85569fe5f2298a3536ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a594cd950e1ae2eb2c19eccf309f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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