解题方法
1 . 已知函数
.
(1)求
的极值;
(2)若
有两个相异的实根
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cecb0f4afcfbea411f32c0f81cebd1a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b217e1a0e031a93520a1483a2c598957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20f84136e680328877f30b2943aaf21.png)
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解题方法
2 . 已知
且满足
,若
恒成立,则实数
的取值范围为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d812643e080d4d447fab7fe2ae2646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384bcd5b965e5204e33ddbd1d45a9b47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014d657e1b5a76a69856e2ed972b9cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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3 . 在平面直角坐标系
中,动点
与两点
连线斜率分别为
,且满足
,记动点
的轨迹为曲线
.
(1)求曲线
的标准方程;
(2)已知点
为曲线
在第一象限内的点,且
,若
交
轴于点
交
轴于点
,试问:四边形
的面积是否为定值?若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3c9967968279271d8cf1f9444c0ac1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4afe8066b2119e0b196f01455076dab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff6b7670302e7015123b9446afab1f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd3b5486425da4e2025804d372dd654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5b62ea69808e36e57db3cf2583f118.png)
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2022-11-28更新
|
794次组卷
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3卷引用:重庆市三校2023届高三上学期11月拔尖强基联合定时检测数学试题
4 . 我们把一组焦点相同的双曲线称为“同焦双曲线”.已知双曲线
与双曲线
为“同焦双曲线”,双曲线
的左右焦点分别为
,过点
的直线与双曲线
的右支交于
两点,
与
轴相交于点
的内切圆与边
相切于点
.若
,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca77107f964a5d06be7489c080c2b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7638c88f01d609d79947033ed4ff36a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f5f4ad0caac5a0fecb64f3908d2290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0345b4fa3aad9d2cb6d404bb4165a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5a64bcb77f5f64e4af6930c249a270.png)
A.双曲线![]() ![]() |
B.若直线![]() ![]() ![]() |
C.![]() |
D.记![]() ![]() ![]() ![]() |
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名校
解题方法
5 . 已知椭圆的右顶点为
,左、右焦点分别为
,直线
与椭圆
交于
,当
与
重合时,点
在
轴上的射影为
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6bd21a21a429c595ca5b1d94b567be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4069db6294de3f250cd18bf1b0c2034e.png)
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2022-11-28更新
|
396次组卷
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3卷引用:重庆市第一中学校2022-2023学年高二上学期期中数学试题
名校
6 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
时,求
的极值;
(2)若
,函数
与
轴有两个交点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c62b7cbb2fd9977ff33cadebad3d0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](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/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
7 . 已知函数
.
(1)求曲线
在点
处的切线方程;
(2)证明,对
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/304a82aaff8eb5f4e652073b9891d70a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)证明,对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fa1687fcb43e90a58dab16f544292b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26976bb7d1ce4fafcb3c86d391ab9d9f.png)
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2022-11-27更新
|
1237次组卷
|
8卷引用:重庆市万州第二高级中学2023届高三上学期12月月考数学试题
名校
解题方法
8 . 设定义在R上的函数
与
的导函数分别为
和
,若
,
,且
为奇函数,则下列说法中一定正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6cbd64291fa53ffec2592a50559e9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c59efaca2fa9cc675c3e1dd9d4d7b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6d578f9c98ce402d4cf6e4a23281c5.png)
A.![]() | B.函数![]() ![]() |
C.![]() | D.![]() |
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2022-11-25更新
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1370次组卷
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10卷引用:重庆市2023届高三上学期第一次质量检测数学试题
重庆市2023届高三上学期第一次质量检测数学试题海南省海口中学2023届高三上学期9月摸底考试数学试题山东省青岛市青岛第五十八中学2022-2023学年高三上学期10月月考数学试题山东省济宁市微山县第二中学2022-2023学年高三上学期期中数学试题广东省广州市从化区第三中学2023届高三上学期第三次段考(11月)数学试题山东省济宁市兖州区2022-2023学年高三上学期期中数学试题湖南省永州市江华瑶族自治县第一中学2022-2023学年高三上学期12月月考数学试题湖南省长沙市长郡中学2022-2023学年高三上学期月考(二)数学试题齐鲁名校2023届高三第二次质量检测数学跟踪测试题(已下线)2023年高三数学押题密卷三
9 . 双曲线
的左、右顶点分别为
,
,过点
且垂直于
轴的直线
与该双曲线
交于点
,
,设直线
的斜率为
,直线
的斜率为
.
(1)求曲线
的方程;
(2)动点
,
在曲线
上,已知点
,直线
,
分别与
轴相交的两点关于原点对称,点
在直线
上,
,证明:存在定点
,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f5d9add1a8ef4d5d520f9bcc568d42.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/269a51e0f77f63bae2df3dc8b1d4f455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319a01218514917e446dfc807a625ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7219ba6e1a9dfe3f11dc3462be1a9fd.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)动点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de78b493bc2cc9696c584325c22ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7555f635da615b09b7e2f08ddbeaf1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eebe4d3c925e04eb4a5e0318143482fb.png)
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2022-11-25更新
|
967次组卷
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5卷引用:重庆市万州第二高级中学2023届高三上学期12月月考数学试题
名校
解题方法
10 . 已知
定义域为
,对任意
,
都有
.当
时,
,且
.
(1)求
的值;
(2)判断函数
单调性,并证明;
(3)若
,
都有
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f370a1d4dd341e5ab1774a66c66c1204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bf20a3e9d3e9f83d8a0f1be4f3486be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d5a0e25aebe1cc182d2247ed344652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1233d79e389ea5a4047cf03e6ba1b1f4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/535d3f599458ed9865ae86ff38048f5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24eb36914c5d05da7d3e23900f0b4124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060ea8f707ee072bfef102869c329674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2022-11-24更新
|
1157次组卷
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3卷引用:重庆市育才中学校2022-2023学年高一上学期期中数学试题