名校
1 . 已知函数
.
(1)若过点
可作曲线
两条切线,求
的取值范围;
(2)若
有两个不同极值点
.
①求
的取值范围;
②当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b30e674c62fd9e25645b3984827759a6.png)
(1)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e868d1326bf73ac658885d4936bbe04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7913a814e2c4ba5e643af885b6ff0efb.png)
您最近一年使用:0次
2024-06-11更新
|
600次组卷
|
4卷引用:安徽省六安第一中学2024届高三下学期质量检测(三 )数学试卷
2 . 已知抛物线C:
(
)的准线与圆O:
相切.
(1)求C的方程;
(2)设点P是C上的一点,点A,B是C的准线上两个不同的点,且圆O是
的内切圆.
①若
,求点P的横坐标;
②求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
(1)求C的方程;
(2)设点P是C上的一点,点A,B是C的准线上两个不同的点,且圆O是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94745b50f9315e478ab5cc64cf9988ae.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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2024-04-19更新
|
636次组卷
|
3卷引用:安徽省六安市六安第一中学2024届高考模拟预测数学试题(四)
名校
解题方法
3 . 已知在平面直角坐标系
中,抛物线
的焦点
与椭圆
的一个顶点重合,点
是椭圆
上任意一点,椭圆
的左、右焦点分别为
,
,且
的最大值为
.
(1)求椭圆
的标准方程;
(2)过抛物线
上在第一象限内的一点
作抛物线
的切线,交椭圆
于A,B两点,线段AB的中点为
,过点
作垂直于
轴的直线,与直线OG交于点
,求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67c5569aa05c7659ce75513f9281ebc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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名校
解题方法
4 . 已知函数
在
上为奇函数,
,
.
(1)求实数
的值;
(2)若对任意
,
,不等式![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a761ce7b2ab701376593bda11531de.png)
都成立,求正数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bbe38c0bfa0dcbb845a38777063b42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5caabda288fc01cc168938846eec5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a761ce7b2ab701376593bda11531de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff98574f62933ec7220fd8e7b091458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2024-02-04更新
|
480次组卷
|
2卷引用:安徽省六安第二中学2023-2024学年高一上学期期末考试数学试卷
2023·全国·模拟预测
5 . 一类项目若投资1元,投资成功的概率为
.如果投资成功,会获得
元的回报
;如果投资失败,则会亏掉1元本金.为了规避风险,分多次投资该类项目,设每次投资金额为剩余本金的
,1956年约翰·拉里·凯利计算得出,多次投资的平均回报率函数为
,并提出了凯利公式.
(1)证明:当
时,使得平均回报率
最高的投资比例
满足凯利公式
;
(2)若
,
,求函数
在
上的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44fed1be8b7e50f18cb90077d9fce8e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893e658908683584084ea8cd2b1abb23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e4dfb68af91a58e45ca8596abc3d96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821289d70c0fb192f97cd7e0c4030d3b.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882d11ef98daf356e7ce70c24d4b9cf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25770560bdfb28b2b79f2900084057e8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f970f380a12c843bb4a74ff34a15b2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee70e500750f7aeef9a15557433ad3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/083479b94380e8d659eff92d10a1989d.png)
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2024-01-17更新
|
834次组卷
|
5卷引用:安徽省六安市金寨第一中学2024届高三上学期期末适应性考试数学试题(二)
名校
解题方法
6 . 已知点
在双曲线
上.
(1)双曲线上动点Q处的切线交
的两条渐近线于
两点,其中O为坐标原点,求证:
的面积
是定值;
(2)已知点
,过点
作动直线
与双曲线右支交于不同的两点
、
,在线段
上取异于点
、
的点
,满足
,证明:点
恒在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be3ad3dd6803d92df6ff8a80cd35095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2702066c515f9b77353cfba5f9e33c0.png)
(1)双曲线上动点Q处的切线交
![](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/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb41efe7bf6a0c35c940d68d85bd928a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad01b0639b0b618c9128df2a5d1315c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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2023-05-17更新
|
1090次组卷
|
4卷引用:安徽省舒城中学2023届仿真模拟卷(二)数学试题
安徽省舒城中学2023届仿真模拟卷(二)数学试题(已下线)专题3.9 圆锥曲线中的定点、定值、定直线问题大题专项训练【九大题型】-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)专题突破卷23 圆锥曲线大题归类山东省青岛市青岛第二中学2023-2024学年高二上学期期中数学试题
名校
7 . 已知
是函数
在其定义域上的导函数,且
,
,若函数
在区间
内存在零点,则实数m的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51a82f33a5187708abf2b21ced6db5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0821c40e176dba970b362f6bd1540e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb53ebe60a1c78ad40f5f34ebf0e168f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
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2023-05-12更新
|
952次组卷
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3卷引用:安徽省六安市六安二中教育集团2024届高三上学期第二次(10月)月考数学试题
名校
解题方法
8 . 已知函数
,函数
是定义在
的可导函数,其导数为
,满足
.
(1)若
在
上单调递减,求实数
取值范围;
(2)对任意正数
,试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357734fbcdf1dfee083990962f7a87e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e137c225bfacce424b961b9bd6fd0b4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)对任意正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfb5f131e42bf2f78f7abbc1cad2eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982e7ec262ba657f72bdc33e0ed2b32e.png)
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2022-12-20更新
|
546次组卷
|
2卷引用:安徽省六安第二中学2022-2023学年高三上学期第四次月考数学试题
名校
9 . 已知函数
.
(1)当
时,求曲线
与
的公切线方程;
(2)讨论方程
实根的个数;
(3)若
有两个不等实根
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f032ad18b0ecc6defbccc525b1d72f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)讨论方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b8da276e3d8eccba292d329122dca1.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8b8da276e3d8eccba292d329122dca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4187c2c5f8176976865728ead5580518.png)
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名校
10 . 若函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc8811c61e45328fe439cff1ddcfa4b.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2022-06-29更新
|
1949次组卷
|
6卷引用:安徽省舒城中学2023届仿真模拟卷(一)数学试题
安徽省舒城中学2023届仿真模拟卷(一)数学试题浙江省金华十校2021-2022学年高一下学期期末数学试题广东省广州六中2023届高三上学期10月月考数学试题山东省青岛市莱西市第一中学2022-2023学年高三上学期12月月考数学试题浙江省宁波市奉化区九校联考2022-2023学年高二下学期期末模拟数学试题(已下线)第四章 导数与函数的零点 专题三 复合函数零点问题 微点3 复合函数零点问题综合训练