1 . 已知
为坐标原点,双曲线
.
上一点
处的切线与
的渐近线交于点
,
,且
的面积为
.
(1)求
;
(2)若过点
的另一条直线与
的渐近线交于点
,
,且
,直线
与圆
相切,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53977ab088f164e44a841b2628b7523c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若过点
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/288399a4bd34af6663e020b93a53c9ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047a0dadd00cdcdb69c01997801c9326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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名校
2 . 已知函数
有三个零点,且
的图像关于直线
对称,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
__________ ;
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42266b2ff7eeda58bd87ccff4ec8bd14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b334dafda377c3db77647c8cf1e95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ccd4162c7d09f970cb77cadacdbe521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-11-22更新
|
634次组卷
|
2卷引用:江苏省"清宵一数"2022-2023学年高三上学期11月第二次学情调研数学试题
3 . 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
|
1125次组卷
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4卷引用:江苏省南通市2022-2023学年高三上学期第一次质量监测数学试题
名校
解题方法
4 . 已知函数
.
(1)当
时,证明
;
(2)若
存在极值点
,且对任意满足
的
,都有
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa5e01a42421e4aabee073b6f552f18.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb1dc30d4b297c6d5d0d6d91eab1e3b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbf8da534490147db4fee75f71a4c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31cdc61764eef3fbe2dc5fafaa2efb39.png)
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2022-07-25更新
|
1649次组卷
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6卷引用:江苏省盐城中学2022届高三下学期5月仿真模拟数学试题
江苏省盐城中学2022届高三下学期5月仿真模拟数学试题浙江省名校协作体2022-2023学年高三上学期适应性联合考试数学试题重庆市开州区临江中学2023届高三上学期入学考试数学试题(已下线)专题10 导数压轴解答题(综合类)-2(已下线)广东省2022届高三一模数学试题变式题17-22(已下线)专题22极值点偏移问题
5 . 已知函数
.
(1)求函数
的单调区间;
(2)若不等式
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb727c12898baef8941abfb6330a6ce8.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c9008a8122ebaba65a0fe52203870a.png)
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2022-05-30更新
|
533次组卷
|
2卷引用:江苏省2022届高三高考前临门一脚数学试题
6 . 已知
,
.
(1)讨论
的单调性;
(2)若函数
与
的图象恰有一个交点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c8c5acc4ae9b1e5aca676b614833d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3056096285f2126ebfbb9127c396de44.png)
(1)讨论
![](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/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-05-29更新
|
1100次组卷
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4卷引用:江苏省南京师范大学附属中学2022届高三下学期5月模拟数学试题
江苏省南京师范大学附属中学2022届高三下学期5月模拟数学试题江苏省宿迁市泗洪县洪翔中学2022-2023学年高三上学期暑期学情检测数学试题(已下线)江苏省南通市如皋市2022-2023学年高三上学期10月诊断调研测试数学试题(已下线)江苏省南通市如皋市2022-2023学年高三上学期期中模拟数学试题
名校
解题方法
7 . 已知函数
.
(1)求证:
;
(2)若
恒成立,求实数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8469ec6106638c7e8ea542cfa4ffc0.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d6848b0e6b6315bb84006d418e0702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-05-28更新
|
712次组卷
|
2卷引用:江苏省南京市教学研究室2022届高三下学期高考前辅导数学试题
8 . 已知F1(-
,0),F2(
,0)为双曲线C的焦点,点P(2,-1)在C上.
(1)求C的方程;
(2)点A,B在C上,直线PA,PB与y轴分别相交于M,N两点,点Q在直线AB上,若
+
,
=0,证明:存在定点T,使得|QT|为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
(1)求C的方程;
(2)点A,B在C上,直线PA,PB与y轴分别相交于M,N两点,点Q在直线AB上,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6799b234237333b0efa331d98f0374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2baf4912377de5ce25b97d190b93b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc2940b5462de27b64430c1a02b4f92c.png)
您最近一年使用:0次
2022-05-27更新
|
4239次组卷
|
12卷引用:江苏省南通、苏北部分学校2022届高三下学期第四次调研考试数学试题
江苏省南通、苏北部分学校2022届高三下学期第四次调研考试数学试题江苏省宿迁市泗洪县洪翔中学2022-2023学年高三上学期暑期学情检测数学试题第3章 圆锥曲线与方程(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(苏教版2019选择性必修第一册)湖北省新高考联考协作体2021-2022学年高二下学期期末数学试题湖北省孝感市2021-2022学年高二下学期期末数学试题(已下线)重难点15七种圆锥曲线的应用解题方法-2(已下线)专题22 圆锥曲线中的定点、定值、定直线问题 微点4 圆锥曲线中的定点、定值、定直线综合训练江苏省南京市第一中学2023届高三下学期2月期初考试数学试题(已下线)第12讲 双曲线(5大考点)-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)(已下线)考向36 圆锥曲线中的定点、定值问题(重点)(已下线)大题强化训练(15)(已下线)专题3-4 双曲线大题综合10种题型归类(讲+练)-【巅峰课堂】2023-2024学年高二数学热点题型归纳与培优练(人教A版2019选择性必修第一册)
名校
9 . 已知函数
=e2x,
,m>0,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca4be345087f993a4078e16c16608e2.png)
(1)若函数
有两个零点,求实数m的取值范围;
(2)若直线
是曲线
=e2x的一条切线,求证:a>b,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5734d093f305e687e303a62a6860f790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca4be345087f993a4078e16c16608e2.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d733483fdf7269db1e357c6207d2747.png)
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10 . 函数
.
(1)求函数
在
上的极值;
(2)证明:
有两个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e76bf15f491fcfbe224efb7f087207.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e622aa8db52df07722b98670338c8d7c.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d82e6095b65b52ae96066d68868ea5.png)
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