解题方法
1 . 已知双曲线的右顶点为
,过点
且与
轴垂直的直线交一条渐近线于
.
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0efd501e4a665e762a8b9b381f561a98.png)
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名校
2 . 已知函数
.
(1)若
,求
的极小值;
(2)若过原点可以作两条直线与曲线
相切,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf532002d16eb7fa80f85990ff8a355e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34b5175d52cccc0bc122a31f5b78b885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若过原点可以作两条直线与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-03-08更新
|
1327次组卷
|
2卷引用:江苏省宿迁市2024届高三下学期调研测试数学试题
解题方法
3 . 已知函数
能表示为奇函数
和偶函数
的和.
(1)求
和
的解析式;
(2)利用函数单调性的定义,证明:函数
在区间
上是增函数;
(3)令
(
),对于任意
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d938482f0bd0d62720f1175b128159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)利用函数单调性的定义,证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6687058d9afa67f1f270d2a06b8b1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e32125207addc3fdb92ceb0ec80ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef17553c1d08bc53ef515daf8b51b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
4 . 已知常数
为非零整数,若函数
,
满足:对任意
,
,则称函数
为
函数.
(1)函数
,
是否为
函数﹖请说明理由;
(2)若
为
函数,图像在
是一条连续的曲线,
,
,且
在区间
上仅存在一个极值点,分别记
、
为函数
的最大、小值,求
的取值范围;
(3)若
,
,且
为
函数,
,对任意
,恒有
,记
的最小值为
,求
的取值范围及
关于
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a6c0fddb9074dfc96be03b4aa24d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1678002c227b520668ab2b976cdfaa3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d79a8b8500b2313a5b08a023d90b15.png)
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4bf72626042d976d413196215876684.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c8381377b90826897eb4bf16cb3bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e817f37f5a814e856ebc4a16d676ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71f6b7d80e4316967fdaea810895317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ae7f07dbd9023f19556fe1e88414f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1e0cac3f562e5b5b952b8231bb91c7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fb2bc63bd8e38e371284aea1fb08861.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572b3dcb438834635f79b2544934af84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c765461ae1a6c70f5cbdcb6c932a22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3367bd41ff428d7a608511cfb1f3cb11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b97a0de833ddcd45995ff3286b5d266b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f804646698060703c5458ff5637c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f804646698060703c5458ff5637c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023-04-20更新
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7卷引用:江苏省宿迁市沭阳如东中学2023-2024学年高二下学期阶段测试(三)数学试卷
江苏省宿迁市沭阳如东中学2023-2024学年高二下学期阶段测试(三)数学试卷上海市徐汇区2023届高三二模数学试题(已下线)重难点04导数的应用六种解法(1)(已下线)第六章 导数与不等式恒成立问题 专题十二 恒成立问题综合训练(已下线)2024年高考数学二轮复习测试卷(新题型,江苏专用)(已下线)信息必刷卷01(江苏专用,2024新题型)(已下线)专题09 导数及其应用 压轴题(六大题型)-备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)
名校
解题方法
5 . 在平面直角坐标系
中,已知双曲线
的离心率为
,直线
与双曲线C交于
两点,点
在双曲线C上.
(1)求线段
中点的坐标;
(2)若
,过点D作斜率为
的直线
与直线
交于点P,与直线
交于点Q,若点
满足
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db0a1cbf7b0ed76c443b953af8734d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cda5a4c295b2817b357e641564ef186.png)
(1)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f0010d2fa7cad70724388250268a412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232ba5b0b0fc22164db67956c5776e5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b7b4084febd6cb00a48327825793969.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ebdd81fbc0cc7797bf036b7f3cb6b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9868d97a121e6fb0f8e7c9007dc7e25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6009b5e4e6fab6e686645e4e680f0935.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708dcc261cb34949749ec6494abe7bef.png)
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2023-03-24更新
|
1081次组卷
|
2卷引用:江苏省宿迁市泗阳中学2023届高三下学期3月阶段模拟测试数学试题
名校
解题方法
6 . 已知函数
.
(1)若
,求函数
的极值;
(2)当
时,若对
,
恒成立,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd04001d68fb2c7bce31c220f98a8bfd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f832d9cca2d5c9d76d38374e2a258d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61451cc73883c93bc9ab3ab00cae2d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f15802a8683020919d225220fcc8681.png)
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2023-03-18更新
|
413次组卷
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4卷引用:江苏省宿迁市泗阳中学2024届高三上学期12月阶段测试数学试题
名校
解题方法
7 . 设F是抛物线
的焦点,直线
与抛物线C交于
两点,O为坐标原点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4300cdebb4dee5a135c5ed2b706b9cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
A.![]() |
B.![]() |
C.P为抛物线上异于A、B的点,直线l与准线交于点T,当![]() ![]() ![]() ![]() |
D.若在抛物线上存在唯一一点Q ![]() ![]() ![]() ![]() |
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8 . 数列
满足
,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ba3f90c7c48ad9d0316b7cea3e2b7c.png)
A.若![]() ![]() ![]() |
B.若存在无数个自然数![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() |
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6卷引用:江苏省宿迁市沭阳县建陵高级中学2022-2023学年高三上学期期中数学试题
9 . 设函数
,
.
(1)若直线
是曲线
的一条切线,求
的值;
(2)证明:①当
时,
;
②
,
.(
是自然对数的底数,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc1b193aa193153eb402df8560778e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad0ec3c50f8ff3bbb30ba0a0962073f2.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87490be8d0cdb7bc6c39d1a37f3bc335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)证明:①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca542e78b7d77d008c9c4752afa91a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb31e419ea4e0ec8f06d8cb4e348debc.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4dacb2a0080a87354011933ee07008f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25da8298b6a96d627f3e8c990e55f0c.png)
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2022-09-19更新
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4卷引用:江苏省宿迁市沭阳如东中学2022-2023学年高三上学期9月阶段测试(三)数学试题
名校
10 . 已知函数
,
(
).
(1)讨论函数
的单调性;
(2)证明:当
时,
在
上恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f213112b534bc6fa89fd57b2b09134be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc93ac476e33aa4480dea0ba815a192a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8433ca05d7bf0987ee16c0f3b506dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4acda6b6464db27e1ec18a1522406d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
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2022-08-26更新
|
558次组卷
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4卷引用: 江苏省宿迁中学2022-2023学年高二下学期入学检测数学试题
江苏省宿迁中学2022-2023学年高二下学期入学检测数学试题吉林省八所省重点中学2021-2022学年高二下学期期末联考数学试题广东省东莞实验中学2023届高三上学期月考一数学试题(已下线)高二上学期期末【压轴60题考点专练】(选修一+选修二)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)