名校
1 . 已知函数
.
(Ⅰ)求曲线
在点
处的切线方程;
(Ⅱ)求证:存在唯一的
,使得曲线
在点
处的切线的斜率为
;
(Ⅲ)比较
与
的大小,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f150d5ef78b3298229880b5e327685.png)
(Ⅰ)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(Ⅱ)求证:存在唯一的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0324fecb070287715e3e8f2322056922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0573a6bcc480a91a43126d01bc19eeae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bd30bbe4130d3161d55011d4cf9a3d0.png)
(Ⅲ)比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554231a67ae07a50e2510f42c3250136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b708034aa1e680d6b14ce2133650a85.png)
您最近一年使用:0次
2018-01-21更新
|
1255次组卷
|
10卷引用:北京市第一七一中学2022届高三10月月考数学试题
名校
2 . 已知函数
.
(1)讨论
的单调性;
(2)当
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/054ecedf0ec5db95a6669fdd2080588c.png)
(1)讨论
![](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/2bdb8989903529182889fdf2e984dac9.png)
您最近一年使用:0次
2023-02-17更新
|
4122次组卷
|
15卷引用:北京九中2022届高三10月月考数学试题
北京九中2022届高三10月月考数学试题北京市第八中学怡海分校2022届高三12月月考数学试题【区级联考】北京市顺义区2019届高三期末理科数学试题河南省焦作市普通高中2020-2021学年高二下学期期中考试试题文科数学福建省龙岩第一中学2022届高三上学期第一次月考数学试题北京师范大学第二附属中学2023届高三上学期10月月考数学试题内蒙古赤峰市宁城县2019-2020学年高二上学期期末数学(理)试题陕西省西安市鄠邑区2023届高三下学期第一次质量检测理科数学试题广东省惠州市实验中学2023届高三下学期3月月考数学试题湖北省武汉市第四十九中学2022-2023学年高二下学期3月月考数学试题天津市静海区第一中学2022-2023学年高二下学期3月学业能力调研数学试题(已下线)第5章 导数及其应用(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(沪教版2020选择性必修第二册)西藏日喀则市2023届高三第一次联考模拟数学(理)试题宁夏回族自治区石嘴山市第三中学2024届高三下学期第三次模拟考试理科数学试题云南省昆明市昆明师范专科学校附属中学2023-2024学年高二下学期3月学业质量监测数学试题
名校
解题方法
3 . 如图,已知椭圆
长轴长为4,离心率
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/30/28a97491-fffa-4653-a4b8-b839838112ec.jpg?resizew=219)
(1)求椭圆C的标准方程;
(2)点
为椭圆C上一点,设
是经过右焦点F的任一弦(不经过点P),直线
与直线
相交于点M,记
的斜率分别为
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/30/28a97491-fffa-4653-a4b8-b839838112ec.jpg?resizew=219)
(1)求椭圆C的标准方程;
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166a8e1bcb93423697696e2ba0409fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca1726d463bd741c904abd9b6589056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7298e9172c5139222535dd653549b9b6.png)
您最近一年使用:0次
2022-10-27更新
|
730次组卷
|
3卷引用:北京市广渠门中学2021-2022学年高二上学期期中数学试题
名校
4 . 已知函数
.
(1)判断函数
在区间
上的单调性,并说明理由;
(2)求证:函数
在
内有且只有一个极值点;
(3)求函数
在区间
上的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1947fd8b1e5fa9096c13256fdb3a23ed.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f00f2f6ab162f9333ec55db195d663b.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc299018cae8bc47faa38c156b355ec6.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311353ec03c12891582f68c4cb757003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/490710d89500a6de8764fd76f8ef8895.png)
您最近一年使用:0次
2022-04-19更新
|
876次组卷
|
10卷引用:北京市海淀区2021届高三下学期期中数学试题
北京市海淀区2021届高三下学期期中数学试题北京市海淀区2021届高三一模数学试题山东省潍坊市2021届高三二模考试数学模拟试题(已下线)押第21题 导数的应用-备战2021年高考数学(文)临考题号押题(全国卷2)江苏省泰州中学2020-2021学年高二下学期期中数学试题北京市第五十七中学2023届高三上学期开学考试数学试题北京市第一零九中学2023届高三上学期十月月考数学试题(已下线)专题03 导数与函数的单调性、极值、最值问题-2022年高考数学毕业班二轮热点题型归纳与变式演练(新高考专用) 江苏省南京航空航天大学苏州附属中学2021-2022学年高二下学期线上期中数学试题(已下线)高二数学下学期期中模拟试卷(第6章-第8章,含数列和导数)-【题型分类归纳】2022-2023学年高二数学同步讲与练(苏教版2019选择性必修第二册)
解题方法
5 . 如图,椭圆
经过点
,且长轴长是短轴长的
倍.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/77e793f5-564c-480b-a2ca-9bca9fe60849.png?resizew=245)
(1)求椭圆
的方程;
(2)经过点
,且斜率为
的直线与椭圆
交于不同的两点
、
(均异于点
),求证:直线
与
的斜率之和为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71885f023172807ad43f2c9a670aa960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/77e793f5-564c-480b-a2ca-9bca9fe60849.png?resizew=245)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
您最近一年使用:0次
2021-12-29更新
|
700次组卷
|
4卷引用:北京顺义区2020-2021学年高二上学期期末期末试题
名校
解题方法
6 . 已知椭圆
过
两点.
(1)求椭圆
的方程;
(2)设
为第三象限内一点且在椭圆
上,直线
与
轴交于点
,直线
与
轴交于点
,求证:四边形
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9157b279e6c8d68b90201b0ea0fe45db.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e53abbd672b82a02c4975f99fbbd2c37.png)
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2021-12-12更新
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1157次组卷
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5卷引用:北京科技大学附属中学2020-2021学年高二上学期期末考试数学试题
7 . 1.已知函数
,
.
(1)讨论函数
的单调性;
(2)当
时,求证:函数
在区间
上有且仅有一个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799e0db4b64f85b168329f91554e1e0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
您最近一年使用:0次
名校
8 . 已知函数
.
(1)讨论
的单调性;
(2)当
时,证明
;
(3)若不等式
恰有两个整数解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29f444db402303c7a0b67abfa0a8332.png)
(1)讨论
![](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/5d0d2761b7298a62a7f56caef88ee3db.png)
(3)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2021-09-03更新
|
680次组卷
|
2卷引用:北京市一零一中学2020-2021学年高二下学期期中数学试题
9 . 已知函数
,曲线
在点
处的切线与直线
垂直.
(1)求函数
的单调区间和极值;
(2)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7da86c33fca8699b4236f19a10de2f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1a686b80b8f109a929f58c2de7201d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37516bfffd06daa07a698b3a495e1eeb.png)
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2021-08-28更新
|
649次组卷
|
3卷引用:北京市海淀外国语实验学校2022届高三9月月考数学试题
解题方法
10 . 已知椭圆
过
点,且
.
(Ⅰ)求椭圆
的方程;
(Ⅱ) 若过
的直线
与
轴交于点
,过点
作直线
,
不垂直于坐标轴且与
不重合,
与椭圆
交于
,
两点,直线
,
分别交直线
于
,
两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c6162828793e697cb1ad643b287c4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234e7679481ec0d01c915b7fbb71891d.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(Ⅱ) 若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6299c1e360a6932b6b6549fa8606cce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468f1f292d17a3a40ff1cafa0a163552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d71f015144ffaf1faec94a259b4a06.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/030c0325fde242e06cee8d270ba89d68.png)
您最近一年使用:0次