1 . 已知椭圆
,圆
.
(1)点
是椭圆
的下顶点,点
在椭圆
上,点
在圆
上(点
异于点
),连
,直线
与直线
的斜率分别记作
,若
,试判断直线
是否过定点?若过定点,请求出定点坐标;若不过定点,请说明理由.
(2)椭圆
的左、右顶点分别为点
,点
(异于顶点)在椭圆
上且位于
轴上方,连
分别交
轴于点
,点
在圆
上,求证:
的充要条件为
轴.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b1cb1359bcb061ce7737fb7e1b34f1.png)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa154ac33703b5c836047b2143697c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0aea8e4a6e524f43f9a13c1ef4fbddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f4fed042a050d47d7f1331605d7923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa0defb1d52e1973c1c6db736574dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c782675efb07943bcee0339945a08711.png)
您最近一年使用:0次
名校
2 . 对于函数
,若存在
,使得
,则称
为函数
的一阶不动点; 若存在
,使得
,则称
为函数
的二阶不动点; 依此类推,可以定义函数
的
阶不动点. 其中一阶不动点简称不动点,二阶不动点也称为稳定点.
(1)已知
,求
的不动点;
(2)已知函数
在定义域内单调递增,求证: “
为函数
的不动点”是“
为函数
的稳定点”的充分必要条件;
(3)已知
,讨论函数
的稳定点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea844642720c083f09f158f56dabccd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b359345c5afa1739bf5ebf8982e1d959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.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/b359345c5afa1739bf5ebf8982e1d959.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374054f44b9a52668f91ac7601e63c06.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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00f94dd5025e18bf38bd8490b55b19ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知函数
![](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/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7b5582e1931243dbb90b7591137f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b239fed4dbe4954bf39b488ddbfdbfee.png)
您最近一年使用:0次
2024-02-20更新
|
1331次组卷
|
4卷引用:重庆市巴蜀中学校2024届高考适应性月考卷(六)数学试题
重庆市巴蜀中学校2024届高考适应性月考卷(六)数学试题(已下线)压轴题函数与导数新定义题(九省联考第19题模式)练(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上海市松江二中2023-2024学年高三下学期5月月考数学试题
3 . 若函数
的图象上的两个不同点处的切线互相重合,则称该切线为函数
的图象的“自公切线”,称这两点为函数
的图象的一对“同切点”.
(1)分别判断函数
与
的图象是否存在“自公切线”,并说明理由;
(2)若
,求证:函数
有唯一零点且该函数的图象不存在“自公切线”;
(3)设
,
的零点为
,
,求证:“存在
,使得点
与
是函数
的图象的一对‘同切点’”的充要条件是“
是数列
中的项”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf5beca5f1a475dbf003bb2e27d51dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf5beca5f1a475dbf003bb2e27d51dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf5beca5f1a475dbf003bb2e27d51dd.png)
(1)分别判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2750eb2ffdae5d0be38bda2ebb51875b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c6e387dd234bb49f53df1668d5e63e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4157d7a3d18b13df5428790499406f7d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039124ad765f2a9d8d3382bdc60a3d6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1551e58c685b32149bffcb9329e710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdab40c21646025ac21019cf6e883c54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a943c3df48c0961838d083e1c34fdbdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fa720a5bafa2bb6ec5c60197e74a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d2fad3eba14b645100f279cf2af2ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
您最近一年使用:0次
4 . 若数列
在某项之后的所有项均为一常数,则称
是“最终常数列”.已知对任意
,函数
和数列
满足
.
(1)当
时,证明:
是“最终常数列”;
(2)设数列
满足
,对任意正整数
.若方程
无实根,证明:
不是“最终常数列”的充要条件是:对任意正整数
,
;
(3)若
不是“最终常数列”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc6de641322c6aeb24e0bbd875e65b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3980f4d5c5ec0f551d7a3c3c0b5ffdc7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914c67ddd60c47e91783929c8bdf8ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b26218ecae19cc13017d561c01d69f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36737370e7f4231ebdd27c957f47f45b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd689fbacfbe6c1bd0953521bbf3638b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8f2cc86844dc647bfb33344781e75a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66c77ea288be5bfb4445a76a2429aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
您最近一年使用:0次
5 . 定义:设
和
均为定义在
上的函数,它们的导函数分别为
和
,若不等式
对任意实数
恒成立,则称
和
为“相伴函数”.
(1)给出两组函数,①
和
②
和
,分别判断这两组函数是否为“相伴函数”(只需直接给出结论,不需论证);
(2)若
是定义在
上的可导函数,
是偶函数,
是奇函数,
,证明:
和
为“相伴函数”;
(3)
,写出“
和
为相伴函数”的充要条件,证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c325e7c3a16e7e6fe3835e24d093b71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(1)给出两组函数,①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeea68b05083aaf5bc84b63ddea32fab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61c6ee8a90940db217d0ed2202cfa3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d3d9ab1739e4f997071a7d558bb6afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4985909410ebcf6be0cf45b2057c7eaf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e3970e1ef97656c4db82edf2b75b000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2e5e73fcd10764ccd2a44bae179986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c56877b5653c96790a2ae9482f4e55e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
您最近一年使用:0次
名校
解题方法
6 . 若数列
满足:
,且
,则称
为一个
数列.对于一个
数列
,若数列
满足:
,且
,则称
为
的伴随数列.
(1)若
数列
中,
,写出其伴随数列
中
的值;
(2)若
为一个
数列,
为
的伴随数列
①证明:“
为常数列”是“
为等比数列的充要条件;
②求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0b585b9c5b459de9186779aba4030d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.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/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76b0b282d53c9467e0ec983fed79c622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f36f5e8a5983a1413e3f63f35c7cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd8ae4555eacf411d0a8867d9970668.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
①证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/325629d6ef791f80f37af613adcf92fd.png)
您最近一年使用:0次
2023-12-11更新
|
1300次组卷
|
2卷引用:广东省2024届高三数学新改革适应性训练一(九省联考题型)
名校
解题方法
7 . 对于数列
定义
为
的差数列,
为
的累次差数列.如果
的差数列满足
,
,则称
是“绝对差异数列”;如果
的累次差数列满足
,
,则称
是“累差不变数列”.
(1)设数列
:2,4,8,10,14,16;
:6,1,5,2,4,3,判断数列
和数列
是否为“绝对差异数列”或“累差不变数列”,直接写出你的结论;
(2)若无穷数列
既是“绝对差异数列”又是“累差不变数列”,且
的前两项
,
,
(
为大于0的常数),求数列
的通项公式;
(3)已知数列
:
是“绝对差异数列”,且
.证明:
的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a07d79baaaa6a46766269084b5d01da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5dc94bb96914a455346621c4514d0a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da1eb1dee559bfe3573398ea8dbcf9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf4b1ce2ae73fb3c886bb24fe4ec47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eb15cd939b6af954ad0c7e1b0c021a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d64495cfce1ec393b97f1a4cf68435c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
(2)若无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1bae03ee4ac75dacfb026290e4207dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f108d4cbb79fbc793f2dfc9209b9436d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6807e876b1cbaa47bf0f38dedcce8b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(3)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2593f5cb146ebaac56d3127b56595d4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae58bfd8ae5f887ff5c45432350b184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f76a020285428cecc4342afede16a80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53eaa658e2f62d834ab305f410d6ca49.png)
您最近一年使用:0次
8 . 已知集合
,对于集合
的非空子集
.若
中存在三个互不相同的元素
,
,
,使得
,
,
均属于
,则称集合
是集合
的“期待子集”.
(1)试判断集合
,
是否为集合
的“期待子集”;(直接写出答案,不必说明理由)
(2)如果一个集合中含有三个元素
,
,
,同时满足①
,②
,③
为偶数.那么称该集合具有性质
.对于集合
的非空子集
,证明:集合
是集合
的“期待子集”的充要条件是集合
具有性质
;
(3)若
的任意含有
个元素的子集都是集合
的“期待子集”,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a32bb35170ebe4aba4d96ad30fcfe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.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/20d6fc9b90f370fbb27552876b650f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/980ab4deb9e7f2bc9288787f5243a4d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1176ec378d071e8972ffaa3f944952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(1)试判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca1c611cfb42aba676bc20f876f8f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570507469628d759e4ebf323fadf79c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f30f56664446f32dbbc2c5f12a99374.png)
(2)如果一个集合中含有三个元素
![](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/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d561cdf17d3a6d7d57af719cb6100c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55de080a3c1313bbd6ea5c17307c723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1433c8103033c67232f2f9ae189608d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18392c5a07408fd70ddee8a30f705305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-03-21更新
|
1042次组卷
|
6卷引用:北京市丰台区2023届高三一模数学试题
北京市丰台区2023届高三一模数学试题专题12压轴题汇总(10、15、21题)专题01集合与常用逻辑(已下线)北京市丰台区2023届高三下学期3月一模数学试题变式题16-21北京卷专题02集合(解答题)(已下线)第一章 集合与逻辑(压轴题专练)-速记·巧练(沪教版2020必修第一册)
名校
解题方法
9 . 令
.
(1)若
,
,试写出
的解析式并求
的最小值;
(2)已知
是严格增函数,
是周期函数,
是严格减函数,
,求证:
是严格增函数的充要条件:对任意的
,
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f389d2b2ea67586fa18c9362e6621b9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1723a3672a6d29807750ac7803ec379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ddac37d332169a34598a63b4634b46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcafc95a0527841c29a58d4f7d85e232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcafc95a0527841c29a58d4f7d85e232.png)
(2)已知
![](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/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef80b434078bf063f1f4c958be301871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b90551ed750a9e91f39d9b5079d9fef.png)
您最近一年使用:0次
10 . 给定正整数m,数列
,且
.对数列A进行T操作,得到数列
.
(1)若
,
,
,
,求数列
;
(2)若m为偶数,
,且
,求数列
各项和的最大值;
(3)若m为奇数,探索“数列
为常数列”的充要条件,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee00267997ecd957562fe62214153ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e972bd6405268bcb111d97039df7c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8743cb652671f7a19a5c9aca1c65a43.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b6e51986fe5d7a7265e0e93adcb4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced4e381e8c3336848b8c436dbc584f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc250de2317c83a904f0ebce5fc2989.png)
(2)若m为偶数,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d14ae78ff7bc3ecb1735171cdeda7f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21548fbce5a8c4385975335a66401bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc250de2317c83a904f0ebce5fc2989.png)
(3)若m为奇数,探索“数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc250de2317c83a904f0ebce5fc2989.png)
您最近一年使用:0次
2022-06-02更新
|
1226次组卷
|
8卷引用:北京市大兴区兴华中学2022届高三三模数学试题
北京市大兴区兴华中学2022届高三三模数学试题北京市第十二中学2022届高三第三次模拟练习数学试题 (已下线)2022年新高考北京数学高考真题变式题13-15题北京市第十二中学2022届高三下学期第三次模拟练习数学试题(已下线)2022年新高考北京数学高考真题变式题19-21题北京市对外经济贸易大学附属中学2023届高三上学期12月月考期末综合测试(一)数学试题北京市日坛中学2023届高三上学期12月月考数学试题(已下线)模块九 数列-2