1 . 设椭圆
,
的离心率是短轴长的
倍,直线
交
于
、
两点,
是
上异于
、
的一点,
是坐标原点.
(1)求椭圆
的方程;
(2)若直线
过
的右焦点
,且
,
,求
的值;
(3)设直线
的方程为
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb340ba1c150c09af10b7d376950018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a087723dd13c3d00f474ba287b47b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104657a7c2bff650e4bfa4ed856640dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5d9c69333838934959395ecf70e0fa.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8686804f0ec59ce9160c26a64a073e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78004248732e95cd7cdae11e1e4c2cb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98209e27a49e69df8d5ab4130c60920a.png)
您最近一年使用:0次
2 . 为了提高学生参加体育锻炼的积极性,某校本学期依据学生特点针对性的组建了五个特色运动社团,学校为了了解学生参与运动的情况,对每个特色运动社团的参与人数进行了统计,其中一个特色运动社团开学第1周至第5周参与运动的人数统计数据如表所示.
若表中数据可用回归方程
来预测,则本学期第11周参与该特色运动社团的人数约为______ .(精确到整数)
周次 | 1 | 2 | 3 | 4 | 5 |
参与运动的人数 | 35 | 36 | 40 | 39 | 45 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3c78c94449ff9171197e82e14fdc6d.png)
您最近一年使用:0次
名校
3 . 若存在使得
对任意
恒成立,则称
为函数
在
上的最大值点,记函数
在
上的所有最大值点所构成的集合为
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6990382f3bd8be4ea77ea659377b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e22ed576560576c840990c6f9827fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d1bdf9d3955fad0976a54cb03b29df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2024-01-19更新
|
1557次组卷
|
3卷引用:上海市普陀区晋元高级中学2024届高三上学期秋考模拟数学试题
4 . 对于一个在区间
上连续的可导函数
,在
上任取两点
,
,如果对于任意的
与
的算术平均值的函数值大于等于对于任意的
与
的函数值的算术平均值,则称该函数在
上具有“M性质”.如果对于任意的
与
的几何平均值的函数值大于等于对于任意的
与
的函数值的几何平均值,则称
在
上具有“L性质”.
(1)如果函数
在定义域内具有“M性质”,求
的取值范围.
(2)对于函数
,若该函数的一个驻点是
,求
,并且证明该函数在
上具有“L性质”.
(3)设存在
,使得
.
①证明:取
,则有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65830dfaf9283417c507bae97933c5ce.png)
②若
,设命题
:函数
具有“
性质”,命題
为严格减函数,试证明
是
的必要条件.
(可用结论:若函数
在区间
上可导,且在区间
上连续,若有
,且
,则
在区间
上存在驻点)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b2a1ef29a4a98f1b793712fe9424bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d34269e6c479d784c8fa90e812b4a4.png)
![](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/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](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/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
(1)如果函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08c076bf43ceb990e6b415e32599ac4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4f19bc4ea459e362a5acaaa82c8cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab8e5280ebca9e7f45e4cdb4769f30b2.png)
(3)设存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4757bb977bdb186160e8f58bcd5464da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc9edb22a22dd339bf9f169e6642169.png)
①证明:取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e1bd630945910eb3dd7148a425d47c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65830dfaf9283417c507bae97933c5ce.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce315caf2fa43a691f1806500b9f3c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2849327037885aabc3512c60d03ecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(可用结论:若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306621a2b3d220bbe34027c1aa503b28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f94345694d4215284c41f87146795ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
您最近一年使用:0次
解题方法
5 . 对于一个三维空间,如果一个平面与一个球只有一个交点,则称这个平面是这个球的切平面.已知在空间直角坐标系
中,球
的半径为
,记平面
、平面
、平面
分别为
、
、
.
(1)若棱长为
的正方体、棱长为
的正四面体的内切球均为球
,求
的值;
(2)若球
在
处有一切平面为
,求
与
的交线方程,并写出它的一个法向量;
(3)如果在球面上任意一点作切平面
,记
与
、
、
的交线分别为
、
、
,求
到
、
、
距离乘积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd48d1ef9e8cd3b7aea60fd95b70fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef1e8a88d934eca5399decc64fdbd43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
(1)若棱长为
![](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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
(2)若球
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5dcb10e84c60bbb67a382349ebeb3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67202feb9b75fb893e9fc70cc1059d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67202feb9b75fb893e9fc70cc1059d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(3)如果在球面上任意一点作切平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
您最近一年使用:0次
6 . 求有___________ 组
、
、
、
(
、
、
、
均为正整数),满足等式
.
![](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/b6a24198bd04c29321ae5dc5a28fe421.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/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab797c5e8378285cff446f8bca5e9012.png)
您最近一年使用:0次
名校
7 . 若曲线
上的点P与曲线
上的点Q关于坐标原点对称,则称P,Q是
,
上的一组奇点.若曲线
(
且
)与曲线
有且仅有一组奇点,则
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fba98327c9fc19b9756766732b33ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060e7930731eddbcfac592b808e9b698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce5e3a606e910cba4f6cff8cc57ce3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-01-13更新
|
1038次组卷
|
5卷引用:上海市普陀区晋元高级中学2024届高三上学期秋考模拟数学试题
8 . 对于函数
,分别在
处作函数
的切线,记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”,同理记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”
(1)设函数
,记
“切线-
轴数列”为
,记
为
的前n项和,求
.
(2)设函数
,记
“切线-
轴数列”为
,猜想
的通项公式并证明你的结论.
(3)设复数
均为不为0的实数,记
为
的共轭复数,设
,记
“切线-
轴数列”为
,求证:对于任意的不为0的实数
,总有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ed953d6e0bd80a5da66552c7bfbcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3d48fa9493a86f262569df235a82ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8292395dc894796602a60486e575a808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ef5756fec38d1b4dc62358b45c3352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e845964df4b271bd7b4cf99ede79be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)设复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bcf306a6aa8554d1d7fc8317f4e946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5f303f666e164582da05968d9d8cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6f044a9b06a7a769e613c977cbfb87.png)
您最近一年使用:0次
2024-01-01更新
|
444次组卷
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7卷引用:上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题
上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题(已下线)模块一专题1【练】《导数的概念、运算及其几何意义》单元检测篇B提升卷(人教A2019版)(已下线)模块二 专题1 与曲线的切线相关问题(已下线)模块二 专题3 与曲线的切线相关问题(人教B版)(已下线)模块一 专题1 《导数的概念、运算及其几何意义》B提升卷(苏教版)(已下线)模块二 专题1 与曲线的切线相关问题(苏教版高二)(已下线)模块二 专题4 与曲线的切线相关问题(高二北师大版)
名校
9 . 对于函数
,把
称为函数
的一阶导,令
,则将
称为函数
的二阶导,以此类推
得到n阶导.为了方便书写,我们将n阶导用
表示.
(1)已知函数
,写出其二阶导函数并讨论其二阶导函数单调性.
(2)现定义一个新的数列:在
取
作为数列的首项,并将
作为数列的第
项.我们称该数列为
的“n阶导数列”
①若函数
(
),数列
是
的“n阶导数列”,取Tn为
的前n项积,求数列
的通项公式.
②在我们高中阶段学过的初等函数中,是否有函数使得该函数的“n阶导数列”为严格减数列且为无穷数列,请写出它并证明此结论.(写出一个即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc50cb09e19e0d2d6aac80e1595c40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51350a90203fcdc2d500a89061b7f52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b211497c206bf64cbccfbc78b88cf284.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85b386e931b512e94ade91181aa8cc2.png)
(2)现定义一个新的数列:在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d3a735f9848d5d727482a7f56d3ad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee64825b2e41c93f1c368eab203a270b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
①若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4888beb7e1e150e0a9ad6b565dc18316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3400dd0b134de441b93009d5b2549e.png)
②在我们高中阶段学过的初等函数中,是否有函数使得该函数的“n阶导数列”为严格减数列且为无穷数列,请写出它并证明此结论.(写出一个即可)
您最近一年使用:0次
2023-12-16更新
|
816次组卷
|
7卷引用:上海市普陀区长征中学2024届高三上学期10月月考数学试题
上海市普陀区长征中学2024届高三上学期10月月考数学试题上海市嘉定区2024届高三上学期质量调研数学试题(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)广东番禺中学2023-2024学年高三第六次段考数学试题广东省广州市番禺中学2024届高三第六次段考数学试题(已下线)信息必刷卷05(上海专用)(已下线)上海市高二下学期期末真题必刷04(压轴题)--高二期末考点大串讲(沪教版2020选修)
10 . 若存在常数
,使得数列
满足
(
,
),则称数列
为“
数列”.
(1)判断数列:1,2,3,8,49是否为“
数列”,并说明理由;
(2)若数列
是首项为
的“
数列”,数列
是等比数列,且
与
满足
,求
的值和数列
的通项公式;
(3)若数列
是“
数列”,
为数列
的前
项和,
,
,试比较
与
的大小,并证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2108ef893c3ef1f8599a4b8ba7083e8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e91406484c332ac8fc96a54c7e187b.png)
(1)判断数列:1,2,3,8,49是否为“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3331574262d23e775c78e1806dd38a.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e91406484c332ac8fc96a54c7e187b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e909fec4d31cce0e352edd6186d7c235.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e91406484c332ac8fc96a54c7e187b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8141d87fb02b08c88b0c9f27f839a7d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4a42272d8dfd41ed6f6594f8c82c03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07812c89c11b5cb96c2eb573e681cbd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1f6e5fb3d02ed5fe61763857e80c43.png)
您最近一年使用:0次
2023-12-14更新
|
1319次组卷
|
10卷引用:上海市普陀区2024届高考一模数学试题
上海市普陀区2024届高考一模数学试题2024届高三新改革数学模拟预测训练二(九省联考题型)(已下线)2024年高考数学全真模拟卷05(新题型地区专用)(已下线)黄金卷05(已下线)新高考预测卷(2024新试卷结构)(已下线)微考点4-1 新高考新试卷结构压轴题新定义数列试题分类汇编湖南省长沙市四县区2024届高三下学期3月调研考试数学试卷(已下线)专题05 数列(四大类型题)15区新题速递(已下线)专题09 导数(三大类型题)15区新题速递(已下线)湖南省长沙市四县区2024届高三下学期3月调研考试数学试题变式题16-19