名校
解题方法
1 . 已知椭圆E:
过
,
两点.
(1)求椭圆E的方程;
(2)已知
,过
的直线l与E交于M,N两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda54f62b47c78ba9aeffb1cc5905319.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e0ea9cc3c956a0ece85df435492668b.png)
(1)求椭圆E的方程;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e0b4cce429003557b051ea0fa2f7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354a4bedfa9edaadcbf18ebc45858f3f.png)
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2023-02-10更新
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806次组卷
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7卷引用:陕西省宝鸡市陈仓区2023届高三二模理科数学试题
2 . 已知函数
.
(1)当
时,求
的单调区间;
(2)证明: 当
时,
对任意的
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20a21999ea818acdfb48d3641f70d3b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明: 当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f5f7a36e251bbc424ccc127ebb2881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c19a97a8b71ca6b8978f7c413f374805.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
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2022-10-14更新
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2卷引用:陕西省咸阳市高新一中2022-2023学年高三上学期第一次质量检测理科数学试题
解题方法
3 . 已知函数
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8d1a34435611f6a59eac3dbfeb6e17.png)
(1)证明:
;
(2)若
,求实数
的取值范围;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67fec6941bc2f2878f5f9d8e118e92dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8d1a34435611f6a59eac3dbfeb6e17.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257e0a13428a004a923b59d092cf77de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8912438e1e35df847d90ca692af44e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb9a04e700bd3ad3b5a35b2c7207b02.png)
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2023-04-09更新
|
344次组卷
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2卷引用:陕西省渭南市2023届高三下学期教学质量检测(Ⅱ)理科数学试题
名校
4 . 已知函数
,
.
(1)讨论函数
的单调性;
(2)若函数
有最小值
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d727d19d680bb7d4bd61861d75f9960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8fd5321376acc2fa6c7be4aa6005b79.png)
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2023-05-20更新
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580次组卷
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2卷引用:陕西省西安市阎良区关山中学2022-2023学年高二下学期第三次质量检测理科数学试题
名校
解题方法
5 . 过抛物线上的点
作直线交拋物线于另一点
.
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a2d2b2b666b03344637a73e05f5226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)过
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.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/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45193c02903d8966f135678c94fd840a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a17f9549fb066fcf191b42ae414c62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7b816eca15d4b7d060013df53edd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
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2023-03-23更新
|
842次组卷
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6卷引用:陕西省榆林市绥德中学2023届高三下学期2月月考理科数学试题
名校
解题方法
6 . 已知双曲线
:
的右顶点为A,О为原点,点
在
的渐近线上,
的面积为
.
(1)求
的方程;
(2)过点Р作直线
交
于M,N两点,过点N作x轴的垂线交直线AM于点G,H为NG的中点,证明:直线AH的斜率为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52d0151288363337e743d5796b952473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点Р作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2023-05-05更新
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|
4卷引用:陕西省西北工业大学附属中学2023届高三下学期第十三次适应性训练文科数学试题
陕西省西北工业大学附属中学2023届高三下学期第十三次适应性训练文科数学试题陕西省西北工业大学附属中学2023届高三下学期第十三次适应性训练理科数学试题福建省福州市2023届高三质量检测数学试题(已下线)考点16 解析几何中的定值问题 2024届高考数学考点总动员【练】
22-23高三上·河南·期末
名校
7 . 已知函数
,其中
是自然对数的底数.
(1)若
在区间
上单调递增,求
的取值范围;
(2)设函数
,证明:存在唯一的正实数
,使得
恰好有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3e2f665b4d59bc905adf15304a27ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c14c4d16c58dffa4ebef6e5b9adf550.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28eb47bf11a209a6521e16bbed6cbdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
您最近一年使用:0次
2023-01-15更新
|
215次组卷
|
3卷引用:陕西省渭南市瑞泉中学2024届高三第六次质量检测数学(理科)试题
陕西省渭南市瑞泉中学2024届高三第六次质量检测数学(理科)试题(已下线)河南省名校联盟2022-2023学年高三上学期1月新未来联考理科数学试题河南省信阳高级中学2022-2023学年高三上学期期末考试理科数学试题
名校
解题方法
8 . 已知双曲线
的右焦点为
,渐近线方程为
.
(1)求双曲线C的标准方程;
(2)设D为双曲线C的右顶点,直线l与双曲线C交于不同于D的E,F两点,若以
为直径的圆经过点D,且
于点G,证明:存在定点H,使
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8639f8fa866c17565dd4f75970665765.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d63f162c4846a76cadee56ae2f42e37c.png)
(1)求双曲线C的标准方程;
(2)设D为双曲线C的右顶点,直线l与双曲线C交于不同于D的E,F两点,若以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce50eeb654ef50f36a582c785f273ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac90c4158636c076ef1d0d45df68be88.png)
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2023-01-10更新
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6卷引用:陕西省部分名校2022-2023学年高二上学期期末理科数学试题
名校
9 . 已知函数
.
(1)讨论
的单调性;
(2)当
时,
恒成立,求
的取值范围;
(3)设
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ac7e3b2727eda190e3db76098b86af.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e2405c4822bceae1cf191edb502d3b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95df8c93263a8feee0ad75231ed8f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8126b60d4b6085eb0f191afeaabf09fb.png)
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2023-03-26更新
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7卷引用:陕西省西安市铁一中学2022-2023学年高二下学期5月月考理科数学试题
陕西省西安市铁一中学2022-2023学年高二下学期5月月考理科数学试题云南省红河州2023届高三第二次复习统一检测数学试题(已下线)专题07 导数(已下线)专题20利用导数研究不等问题(已下线)专题19 押全国卷(理科)第21题 导数四川省成都市树德中学2023届高三三诊模拟数学(理)试题江西省铜鼓中学2022-2023学年高二下学期4月月考数学试题
解题方法
10 . 已知椭圆
,斜率为2的直线
与椭圆交于
两点.过点
作
的垂线交椭圆于另一点
,再过点
作斜率为
的直线交椭圆于另一点
.
(1)若
为该椭圆的上顶点,求点
的坐标;
(2)证明:直线
的斜率为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2023-03-25更新
|
258次组卷
|
3卷引用:陕西省部分名校2023届高三下学期高考仿真模拟文科数学试题