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1 . 已知实数
满足
,设
,则
的最大为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa845bf3a1b8e0b5697889b8560bffaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0986bc3ccec5c0da395bc78f962eed30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0d6f6a62b180f22f0a7963274acdc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
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2 . 已知函数
,对定义域内任意
,都有
,则正实数
的取值可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e354cf156dce1a97956d2421f6a918bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c414c707c8c9c8f8cc7de894b4a40c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.1 | D.![]() |
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2024-04-15更新
|
414次组卷
|
2卷引用:吉林省部分学校2023-2024学年高二下学期4月月考数学试卷
3 . 已知函数
,若对任意的
恒成立,则正实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34e563fb21d07910bbf3bf674d2e6c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d848c18bf4ebef71405d575434e321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 已知函数
.
(1)若
在
处取得极值
,讨论
的单调性;
(2)若存在实数c,使得方程
的三个实数根
满足
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5935439465b9a6ab04657d4288ce035e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07ae0b4264da6a8812454ffd2f20d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若存在实数c,使得方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677c21e324ed0a4ba6af191dff3277be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb47fab19563ac49c5bc07c11b2688b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7728c3702f569ab602be6728fb4503f9.png)
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5 . 莫比乌斯函数在数论中有着广泛的应用.所有大于1的正整数
都可以被唯一表示为有限个质数的乘积形式:
(
为
的质因数个数,
为质数,
),例如:
,对应
.现对任意
,定义莫比乌斯函数
(1)求
;
(2)若正整数
互质,证明:
;
(3)若
且
,记
的所有真因数(除了1和
以外的因数)依次为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e046acc0e785892df1ef03a440b0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5c607987b73502db63f77c9799f4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fe943e1acfb453f41bee79119cce60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38261aad19184a74c797b6b88ffd344d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86cb09df4dbbe40a2b7ed54da17346dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b5872b44498c348c023828ed66e86d1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b2c4263428e2ee419589171f27e23f.png)
(2)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/201e0fbcfb6833c4b1917cfed3096b6f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e468312d09c6563c9094b710a35a65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4a887eaea7f0aac8505ed3b3c0c678.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4811e3603e8790c25aaf91c41d7c7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/202a57af91d5be04e95fcbdb8f2b788f.png)
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2024-03-26更新
|
1274次组卷
|
5卷引用:河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次月考数学试卷
河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次月考数学试卷重庆市乌江新高考协作体2023-2024学年高二下学期第一阶段学业质量联合调研抽测(4月)数学试题(已下线)【人教A版(2019)】高二下学期期末模拟测试A卷湖南省衡阳市2024届高三第二次联考数学试题(已下线)压轴题08计数原理、二项式定理、概率统计压轴题6题型汇总
名校
解题方法
6 . “
”表示实数
整除实数
,例如:
,已知数列
满足:
,若
,则
,否则
,那么下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ea1aed56c455d77bd3c96b9129d1e9.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/20e1c681b27df538bd4742f6cd8298ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cefeddf71dca8ae824328df3f0e5e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c185ce550ab6fa8f0226e237d6d881d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5520432944173c414edf716f22c41067.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3172a2dfbce3ce32fd909ff548e75b26.png)
A.![]() | B.![]() |
C.对任意![]() ![]() | D.存在![]() |
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7 . 如图,将
个整数放入
的宫格中,使得任意一行及任意一列的乘积为2或-2,记将
个整数放入
的宫格有
种放法,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9bbe98100c8067ff36ac536d043a85.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2765e74b2306cee47bb6b641fdb9845c.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767f5a4746f04db68386fac3970b1ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767f5a4746f04db68386fac3970b1ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9bbe98100c8067ff36ac536d043a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2765e74b2306cee47bb6b641fdb9845c.png)
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2023高三·全国·专题练习
8 . 设数列
满足
,
.
(1)证明:
.
(2)设数列
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb2dbc4c08aa70076c1c12daeedcb298.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c31f2f5b97bc76078c101082bb76bb6.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cf1da18d91f7c98086553d157d1a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffb575d8e0365de6ccab0d0645fc78a.png)
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解题方法
9 . 对任意的非空数集
,定义:
,其中
表示非空数集
中所有元素的乘积,特别地,如果
,规定
.
(1)若
,请直接写出集合
和
中元素的个数.
(2)若
,其中
是正整数
,求集合
中元素个数的最大值和最小值,并说明理由.
(3)若
,其中
是正实数
,求集合
中元素个数的最小值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334e66713c1bb166178d5250f85bce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c363cfd3ada27d5756b6f6512f4b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfc0853aa05ca4ea6a80b7db3a9f702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2dd216be69d8aa90c1a09d67f15374d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e88ec106805854932acac7773085e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29b2c411cea591bb0352687b73fa1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9cad3d008dc3dc18be02b702f7937ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0616b5ffd9092ac782e5bb529482a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56729bd5cfde71dd6d04780792a70b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376e5582c1942682ee5ddb3831d09610.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaae479eb6c8af3d600ae81dbf91fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c5330613e7a260dee6b7914ccd0d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376e5582c1942682ee5ddb3831d09610.png)
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2023-06-14更新
|
384次组卷
|
3卷引用:北京市海淀区首都师范大学附属中学2022-2023学年高二下学期期中练习数学试题
10 . 设数列
满足
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f3f46c393e76cbeeed8f3bf50cc713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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