1 . 抛物线C:
,椭圆M:
,
.
(1)若抛物线C与椭圆M无公共点,求实数r的取值范围;
(2)过抛物线上点
作椭圆M的两条切线分别交抛物线C于点P,Q,当
时,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87e61e0a1bc2ab34fe0cd1de9f59b0e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181820d1a015068701cfdbdf48b24c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
(1)若抛物线C与椭圆M无公共点,求实数r的取值范围;
(2)过抛物线上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8adb3358f321cc2c429b9c20674b271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9b38040230a7f5674f13c690e780ade.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
您最近一年使用:0次
2 . 已知函数
,
,记
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699f767ccf837c2bf8019d03451849c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd17ae52ccb646646e43237c0697495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f92ac0144b7ab2c33c46d7347ffe0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f00b23ab45465b96c7d1c385b56080d.png)
A.若正数![]() ![]() ![]() ![]() |
B.若正数![]() ![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.![]() ![]() ![]() |
您最近一年使用:0次
解题方法
3 . 已知定义域为
的函数
,其中
代表不超过
的最大整数.设数列
满足:
是
在
上最大值,数列
满足:
且
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38618cc6b1ffc6c8a84c906260337b3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4737369d70b1a3144eedcb0c924df616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b5cc159f3dfa0534358359ea245338b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb8851954f243423781831867aedbdf.png)
A.![]() ![]() |
B.![]() ![]() ![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
名校
解题方法
4 . 已知正四面体
的棱长为4,点
是棱
上的动点(不包括端点),过点
作平面
平行于
,与棱
交于
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b971ff1b6f62b36cf0b9a641fc419458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942daed6ad022ec1244412405250ec8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5559854fa31f00c55a9fe8c66de6d9.png)
A.该正四面体可以放在半径为![]() |
B.该正四面体的外接球与以![]() ![]() |
C.四边形![]() |
D.四棱锥![]() ![]() |
您最近一年使用:0次
2024-02-28更新
|
389次组卷
|
2卷引用:甘肃省部分学校2024届高三下学期2月开学考试数学试题
名校
5 . 多元导数在微积分学中有重要的应用.设
是由
,
,
…等多个自变量唯一确定的因变量,则当
变化为
时,
变化为
,记
为
对
的导数,其符号为
.和一般导数一样,若在
上,已知
,则
随着
的增大而增大;反之,已知
,则
随着
的增大而减小.多元导数除满足一般分式的运算性质外,还具有下列性质:①可加性:
;②乘法法则:
;③除法法则:
;④复合法则:
.记
.(
为自然对数的底数),
(1)写出
和
的表达式;
(2)已知方程
有两实根
,
.
①求出
的取值范围;
②证明
,并写出
随
的变化趋势.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9265c54f2a96bf290388484cfd0ff47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c75f7dcce2b59c10237868c6715ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c137b971df3492a2001085d98706801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1343590f4aaf6b9e3f3c200e318bfea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43887f94250f6c073e144f2ae39b3021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8baf79cfbc5cc29029ca66632c20775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf1c89ff75dc38ce474a01c4932f8c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff01089fbfd66ae3411b15e54f7a9120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef134baac9bb96324f585c5e532cbefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09df69561e70f6d8a66d32f7ffa8a60d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272a7f552e7d99ab3756c1d4e64fc355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9e8e03d12633cfe6858b8c85047100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d6ee0cf2632c76087f5bce01358ef8.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b0e3a7c0dc3c1143610f60a0fd884f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1343590f4aaf6b9e3f3c200e318bfea0.png)
(2)已知方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18df306af443a02bf538cfc517d4a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-02-21更新
|
1058次组卷
|
3卷引用:微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编
(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编江苏省海安高级中学2023-2024学年高二下学期第二次月考数学试题广东省广州市华南师范大学附属中学2024届高三上学期数学周测试题(12)
名校
6 . 已知函数
.
(1)讨论
的单调性;
(2)设
,
分别为
的极大值点和极小值点,记
,
.
(ⅰ)证明:直线AB与曲线
交于另一点C;
(ⅱ)在(i)的条件下,判断是否存在常数
,使得
.若存在,求n;若不存在,说明理由.
附:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef3e79110067a46276f0869bea25af5.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45dddee525114c09ee0d1205aed6e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b3b54e0dcdc081d45fb3df933cddc29.png)
(ⅰ)证明:直线AB与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(ⅱ)在(i)的条件下,判断是否存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06318573bd8cf7f9b3ff443b31803df5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397471107e2d3a5ccedda940a29a361a.png)
附:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac45788afe168a32cfc51ad8e1429577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b4427f76042503d0ba2302a55fe33d.png)
您最近一年使用:0次
2024-02-20更新
|
972次组卷
|
6卷引用:重庆市第一中学校2023-2024学年高二下学期开学考试数学试题
名校
解题方法
7 . 在平面直角坐标系
中,点
,点A为动点,以线段
为直径的圆与
轴相切,记A的轨迹为
,直线
交
于另一点B.
(1)求
的方程;
(2)
的外接圆交
于点
(不与O,A,B重合),依次连接O,A,C,B构成凸四边形
,记其面积为
.
(i)证明:
的重心在定直线上;
(ii)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f449cadb49859b80c31ef1f68bfe81b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea16ceca816f7d3d50650af141baf42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2024-02-18更新
|
1670次组卷
|
3卷引用:2024届福建省厦门市一模考试数学试题
解题方法
8 . 设
为坐标原点,
为抛物线
上异于
的一点,
,
.
(1)求
的最小值;
(2)求
的取值范围;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9f2b482e8a8e0e1b5c720a3574af70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e24f172a287592897ea4378a2ad29013.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fb8a80473da8d3f571def3f3f34086d.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e66ea801d8df6d13f924cae67fc1db.png)
您最近一年使用:0次
名校
9 . 设
是正整数,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c496b822e4765fc9bb17685f39a4f05.png)
(1)求证:当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb1296f8b1307fd35d219d51f15c242.png)
(2)求证:当
时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c496b822e4765fc9bb17685f39a4f05.png)
(1)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a79d7f73b6128650bf7aed538260c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb1296f8b1307fd35d219d51f15c242.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11e964999066e7ab9780d6a898bd74d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d093aa4e6b898ff1dab1a5b46519eb3.png)
您最近一年使用:0次
2024-02-11更新
|
109次组卷
|
2卷引用:广东省江门市鹤山市第一中学2023-2024学年高二下学期第一阶段考试数学试卷
名校
10 . 已知函数
,将曲线
绕原点逆时针旋转
,得到曲线
.
(1)证明:存在唯一的实数
,使得曲线
是某个函数的图形,并求出
;
(2)取
,设
是曲线
图象上任意一点,将曲线
绕点
逆时针旋转
,得到函数曲线
,设函数
的极小值为
,求
的单调性.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d189c87f1a3881eee96206f2db03157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
(1)证明:存在唯一的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f7dcce39f3d4dc6b7faf84dc1d0a1.png)
(2)取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a302eda25ef93bbdb2d2b7e57083cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1705a3fae62e52b07493feaf96a4a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbcfe228e4177874873adc94f798c3df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d876a0e087d90963d13cddfe06faca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf14fcd881b728f59867440c627e8159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf14fcd881b728f59867440c627e8159.png)
您最近一年使用:0次