名校
解题方法
1 . 把符号
称为二阶行列式,规定它的运算法则为
.已知函数
.
(1)若
,
,求
的值域;
(2)函数
,若对
,
,都有
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5440a1b5d9338efd6976a56432e100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c8894e0b37af5da23a1c1bffb32017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cce928a442f2feb4671b245142ab96.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388d3d213a231cccf854a29eef611d01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5224a7da7fe6bc28971ce4c277f88588.png)
(2)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f504fcfe5b1116cdcdfa37fccae8a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24eb36914c5d05da7d3e23900f0b4124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9e2227004f51fac55c38578e2843acf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4e37ee5f5ea8640aae6193de160c9ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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|
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4卷引用:江西省萍乡市2022-2023学年高一下学期期中数学试题
2 . 已知点
到
的距离是点
到
的距离的2倍.
(1)求点
的轨迹方程;
(2)若点
与点
关于点
对称,点
,求
的最大值;
(3)若过
的直线与第二问中
的轨迹交于
,
两点,试问在
轴上是否存在点
,使
恒为定值?若存在,求出点
的坐标和定值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若点
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e414c3f13e0e28fe2250bf88e33d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d436fc4cde0f6490b25bdd6e476332ed.png)
(3)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8649ce18c628d0e03e72cef541f8284f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d405c7e1ed6ddac33126b8c1cb511b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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|
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7卷引用:江西省萍乡市芦溪中学2021-2022学年高二上学期开学考试数学(理)试题
名校
3 . 已知函数
(e为自然对数的底数)有两个零点.
(1)若
,求
在
处的切线方程;
(2)若
的两个零点分别为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b6e76de4cbccbface43c0069ccd1cfe.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fbb6770e773fcb8318616fbd23e25c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8210703fae32cb9d752f24dc69be7a3.png)
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|
1441次组卷
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7卷引用:江西省萍乡市第二中学2023届高三上学期10月份质量检测数学(理)试题
解题方法
4 . 已知函数
.
(1)证明:当
时,
恒成立;
(2)首项为
的数列
满足:当
时,有
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a930f36a63e67ba5ce2ab3b8320c7eb0.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9518d59e737e3ac698165c5ec17ba636.png)
(2)首项为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbaae3509b29f0bc77e8687702b7484d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b242016eaeac01ac3d573fa1932a3910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4138f481d09d1d1fc962d5a90245a7.png)
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名校
解题方法
5 . 已知函数
,若
,若点
不可能在曲线C上,则曲线C的方程可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a32815a6b7462fc68521ec4620938d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f74fe8b70a97156754d8e878f6607719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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|
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3卷引用:江西省萍乡市上栗中学2022-2023学年高一上学期期末数学试题
名校
解题方法
6 . 正方体
的棱长为
为该正方体侧面
内的动点(含边界),若
分别与直线
所成角的正切值之和为
,则四棱锥
的体积的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc79c14b2ed75664547ddd8ba5b1be9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52091eb745de866044477641a7c55f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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2卷引用:江西省萍乡市2024届高三二模考试数学试卷
名校
7 . 已知函数
,其中
为常数.
(1)讨论函数
的单调性;
(2)若
有两个相异零点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3890541e03e977afe39975143b2794ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b97b295f88972ba1c7e3cefda0885d.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dae74c724114bfeff024dd7b79f5edc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a63c9c4981054fdf544a9d4168684b.png)
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2019-03-26更新
|
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|
3卷引用:【市级联考】江西省萍乡市2019届高三一模考试数学(理)试题
2014·江西宜春·一模
名校
解题方法
8 . 已知函数
,
.
(1)若
在区间
上不是单调函数,求实数
的范围;
(2)若对任意
,都有
恒成立,求实数
的取值范围;
(3)当
时,设
,对任意给定的正实数
,曲线
上是否存在两点
,
,使得
是以
(
为坐标原点)为直角顶点的直角三角形,而且此三角形斜边中点在
轴上?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c067e6d907f6c0fdfa9be70bbc027595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2905c314cbffa446435bd56c760097e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99f1bc6895934a9e2a6d659383ded9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6eefb2d02e54ce0ce4c9931ef774b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd94098e98d90588cb74c1429033a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4133958c09fdd82cda8838c9cf46ccda.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/9efd09912705e08177bc86e839c41b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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7卷引用:【市级联考】江西省萍乡市2019届高三一模考试数学(文)试题
【市级联考】江西省萍乡市2019届高三一模考试数学(文)试题(已下线)2014届江西省宜春市高三考前模拟理科数学试卷(已下线)2015届山东省淄博实验中学高三第一次诊断性考试理科数学试卷湖南师大附中2019届高三月考试题(七)数学(文)【全国百强校】北京市第四中学2019届高三高考调研卷(二)文科数学试题湖南师范大学附属中学2018-2019学年高三第七次月考数学(文)试题山东省济宁市第一中学2020届高三考前冲刺测试(一)数学试题
9 . 已知函数
.
(1)讨论函数
的单调性;
(2)设
,对任意的
,关于
的方程
在
有两个不同的实数根,求实数
的取值范围(其中
为自然对数的底数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b15ebe5c428e0090e6a9f25a7c2d4fb.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02b8527882799f546a2c215bc8777a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcabbea31e31dc15bd21a26c4d62d983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7be1b46382c95c4c02638095d5259a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742268e12c1dd269500286a8d35e3b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6ca12a57481d558b9d33f3f3d1ccc9.png)
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4卷引用:【市级联考】江西省萍乡市2019届高三第一学期期末考试数学文试题
名校
10 . 已知函数
.
(1)讨论函数
的单调性;
(2)若存在
,使得
,试求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d923df82b977d6293b49c53fbeda43.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98482ea7b98e0f06e72664e78389e4db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e856dd7407c2fad6594228317e3d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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3卷引用:江西省萍乡市莲花中学2019-2020学年高二下学期月考数学(理科)试题
江西省萍乡市莲花中学2019-2020学年高二下学期月考数学(理科)试题2017届内蒙古包头市高三下学期第一次模拟考试数学(理)试卷(已下线)第七章 导数与不等式能成立(有解)问题 专题四 双变量能成立(有解)问题的解法 微点1 双变量单函数能成立(有解)问题的解法