1 . 已知函数
,
.
(1)当
时,求
的单调区间;
(2)当
时,记
的极小值点为
,证明:
存在唯一零点
,且
.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f385b23c5ed85f350ffa395cd860f58.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)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc0733cb65fb25e9096618fff3348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697572b42c40f498ed398099c659df1f.png)
您最近一年使用:0次
2024-04-03更新
|
614次组卷
|
2卷引用:湖南省湘潭市2024届高三下学期3月质量检测数学试题
解题方法
2 . 已知椭圆
:
的离心率为
,
为坐标原点,
,
为椭圆C的左、右焦点,点P在椭圆C上(不包括端点),当
时,
的面积为
,
(1)求椭圆C的标准方程;
(2)设点
,
,直线
,
分别与椭圆C交于异于点P的M、N两点,记直线
,
的斜率分别为
,
,求
的值,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2dfb22c6f1c155747100e7536cd1abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb57d84f9bbcb3e30d4ce7e2e1e8604.png)
(1)求椭圆C的标准方程;
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3544997cc034ed882c0d0a3bdbf5f957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
您最近一年使用:0次
2024-03-24更新
|
579次组卷
|
2卷引用:湖南省湘潭市2024届高三下学期3月质量检测数学试题
解题方法
3 . 已知函数
,记函数
,
的值域分别为
,若
,则
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd1a089301386fa8ea80217d6761b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276b142a9d9f0a87425a668dd6501f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-03-24更新
|
413次组卷
|
2卷引用:湖南省湘潭市2024届高三下学期3月质量检测数学试题
解题方法
4 . 已知
,
为双曲线
:
的左、右焦点,点
满足
,N为双曲线C的右支上的一个动点,O为坐标原点,则()
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea7fdd0a77164d3dc0c032e6cb90b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e8e445500f8a9de2c8ead8b2f24b1fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a35b148c043ddff87cc37c8891138187.png)
A.双曲线C的焦距为4 |
B.直线![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2024-03-24更新
|
500次组卷
|
2卷引用:湖南省湘潭市2024届高三下学期3月质量检测数学试题
名校
解题方法
5 . 若
是函数
的一个零点,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c20f960eb0a90dd17e669244ff5e50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff49a05331e84872c0a1e8709d23455b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c30a9f93bd40684daf8c8c4cd9815d47.png)
A.5 | B.4 | C.3 | D.2 |
您最近一年使用:0次
2024-03-13更新
|
795次组卷
|
5卷引用:湖南省湘潭市湘潭县第一中学2024届高三下学期2月月考数学试题
湖南省湘潭市湘潭县第一中学2024届高三下学期2月月考数学试题江苏省苏州市2024届高三上学期学业质量阳光指标调研数学试题(已下线)考点11 倍(半)角公式及其应用 --2024届高考数学考点总动员【练】2024届高三新高考改革数学适应性练习(4)(九省联考题型)广东省2024届高三新改革数学适应性训练六(九省联考题型)
名校
解题方法
6 . 已知椭圆
的两焦点
,且椭圆
过
.
(1)求椭圆
的标准方程;
(2)设椭圆
的左、右顶点分别为
,直线
交椭圆
于
两点(
与
均不重合),记直线
的斜率为
,直线
的斜率为
,且
,设
,
的面积分别为
,求
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5439f5ff9bd5deec0f0ef35c6f605b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f640a856e8f437a88ebd6c8c8f33dda.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98e3c6bf7a865b1cfa79e8592732736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98013a5042685a1db94249e70c62c09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38d0469336f71edd52dc9148c67db052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59c4295f918205f5598ecc9a96d8867.png)
您最近一年使用:0次
2024-01-29更新
|
2004次组卷
|
3卷引用:湖南省湘潭市湘潭县第一中学2024届高三下学期2月月考数学试题
名校
7 . 已知函数
满足:①对任意
,
;②若
,则
.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ab4b75fa22deba7fcbcdcb31dd45b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a9fa465d83ad1ec629bda8b9d1be67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11a069688e4c797fcf527eab15afa82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ca9ba4cbc0d91bc2c6301e9d23d077.png)
A.![]() | B.![]() |
C.若![]() ![]() | D.若![]() ![]() |
您最近一年使用:0次
2024-01-23更新
|
1847次组卷
|
5卷引用:湖南省湘潭市湘潭县第一中学2024届高三下学期2月月考数学试题
名校
解题方法
8 . 已知函数
,设
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01438ba352735a40b4804c6869e134e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4da0b22b4bd41de9f8436ca2b7c3e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f188325294175c1e0efc36f30690aeb4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-10-30更新
|
3296次组卷
|
10卷引用:湖南省湘潭市湘潭县第一中学2024届高三下学期2月月考数学试题
湖南省湘潭市湘潭县第一中学2024届高三下学期2月月考数学试题四川省雅安市2024届高三零诊考试数学(理)试题四川省雅安市2024届高三零诊考试数学(文)试题(已下线)模块二 专题4《三角函数与解三角形》单元检测篇 A基础卷 (人教A)2024年全国普通高中九省联考仿真模拟数学试题(一)湖南省株洲市第二中学2023-2024学年高三下学期开学考试数学试卷(已下线)三角函数的图象与性质(已下线)专题16 三角函数与恒等变换小题(已下线)2024届新高考数学信息卷5四川省内江市威远中学校2023-2024学年高一下学期期中考试数学试题
名校
解题方法
9 . 已知椭圆
的左、右焦点分别为
,
,过点
且垂直于
轴的直线与该椭圆相交于
,
两点,且
,点
在该椭圆上,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cf6cca367ce2afd96d7d951f9587e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17618d8d22ebb3fd6835a7eb139b4f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13683e2ecf2164a0adbfdb9923d210a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/236f52e04ddbd7253f44b97c4756ef9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.存在点![]() ![]() |
B.若![]() ![]() |
C.满足![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
2023-10-09更新
|
1767次组卷
|
7卷引用:湖南省湘潭市湘潭大学附属实验学校2023-2024学年高二上学期11月期中数学试题
10 . 已知椭圆
的离心率为
分别为椭圆
的左右顶点,
分别为椭圆
的左右焦点,
是椭圆
的上顶点,且
的外接圆半径为
.
(1)求椭圆
的方程;
(2)设与
轴不垂直的直线
交椭圆
于
两点(
在
轴的两侧),记直线
的斜率分别为
.
(i)求
的值;
(ii)若
,则求
的面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0070ebce71a1f18e15050a2fed2fcd61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c352227bbb6e8c8f99c4e30185fb5869.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e72b4868bdd8d15dff2211cc49cd31b.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设与
![](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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f367a71f36a7f1a5f263e47b87243f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c65902e35640cf2c8d4111c36b40145.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ac9e4439b8f0c82427e410dbc86735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e43d5fd4e0175a366093cb1219067d57.png)
您最近一年使用:0次
2023-08-01更新
|
646次组卷
|
3卷引用:湖南省湘潭钢铁集团有限公司第一子弟中学2024届高三8月开学考试数学试题
湖南省湘潭钢铁集团有限公司第一子弟中学2024届高三8月开学考试数学试题广东省广州大学附属中学等三校2022-2023学年高二下学期期末联考数学试题(已下线)重难点突破09 一类与斜率和、差、商、积问题的探究(四大题型)