1 . 已知
为实数,用
表示不超过
的最大整数,例如
,
,
.对于函数
,若存在
且
,使得
,则称函数
是
函数.
(1)判断函数
,
是否是
函数;(只需写出结论)
(2)已知
,请写出
的一个值,使得
为
函数,并给出证明;
(3)设函数
是定义在
上的周期函数,其最小周期为
.若
不是
函数,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/7fe1e778c9e668594c42b77459328c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf813e9500eebd474511b865b876ea4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ae4ee70c548e841fd7ceeac3250b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19de314fd662d45db8c1fd91fd4a3244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19ec960e7b486de3916696346501a13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b551072bee20e351f14d362a3f0e5367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa5440f285de4d2f1cf5a0922628541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1982786864f37e6f954e8d70f9970620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次
11-12高三上·北京·期中
解题方法
2 . 设等差数列
的公差
,且
,记
为数列
的前
项和.
(1)若
成等比数列,且
的等差中项为
,求数列
的通项公式;
(2)若
且
,证明:
;
(3)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711cb94d1812369aa4b34da26240bcce.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)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ad29870419d1ca48b69c128fd18b79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e09e5d73c13f4320344a88316556fdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/492b6d3883713fcaa8a4fdd87b87b480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03572b170178d2f675ee43d4eae7e2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994b2b0e9cfdf45933f6425693ddf4d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5539bdee68b5b31f07b9159be844094a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a0f5af5d9b850baa554794f3d0c898.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd514ada2253613f7401286f1e1590a4.png)
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3 . 已知集合
,其中
,
表示和
中所有不同值的个数.
(Ⅰ)设集合
,
,分别求
和
;
(Ⅱ)若集合
,求证:
;
(Ⅲ)
是否存在最小值?若存在,求出这个最小值;若不存在,请说明理由?
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572242164064256/1572242170281984/STEM/c7fe20e4ac1c4268962364a9c78d5c57.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572242164064256/1572242170281984/STEM/415d0667db21473d804637c87278516e.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572242164064256/1572242170281984/STEM/b80feb2852df4ffaa37f0747f6b8690d.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572242164064256/1572242170281984/STEM/04d602e7f4654054af3a25bda4e6f6a5.png)
(Ⅰ)设集合
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572242164064256/1572242170281984/STEM/a1e9ebeaafbb4fcf97e958002f891d66.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572242164064256/1572242170281984/STEM/63de4979fc5a4cb5904dc7395a487042.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572242164064256/1572242170281984/STEM/a3469911ef7943d0b3abf2935748874a.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572242164064256/1572242170281984/STEM/6aded1fde282464d92312137271cbd56.png)
(Ⅱ)若集合
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572242164064256/1572242170281984/STEM/b39018da4d6d485bbef1fe72c82a39b9.png)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572242164064256/1572242170281984/STEM/cc4993dff7444dd09ad3bca91f509471.png)
(Ⅲ)
![](https://img.xkw.com/dksih/QBM/2015/9/25/1572242164064256/1572242170281984/STEM/b80feb2852df4ffaa37f0747f6b8690d.png)
您最近一年使用:0次
12-13高三·湖北孝感·阶段练习
名校
4 . 已知函数
的定义域为
,若
在
上为增函数,则称
为“一阶比增函数”;若
在
上为增函数,则称
为“二阶比增函数”.我们把所有“一阶比增函数”组成的集合记为
,所有“二阶比增函数”组成的集合记为
.
(Ⅰ)已知函数
,若
且
,求实数
的取值范围;
(Ⅱ)已知
,
且
的部分函数值由下表给出,
求证:
;
(Ⅲ)定义集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9e136a097820e1adf36afe51837cef.png)
请问:是否存在常数
,使得
,
,有
成立?若存在,求出
的最小值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e82cc461b9607e08a8b31597f6d26df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21b581dba9cddfa758eb3a030fcc9de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df2ae3a092acc4ed595dea31ea66bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42b6abf0d716fc2c59e1ea2476286ec.png)
(Ⅰ)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9136daaf071e52fd73cbb0d3c2d4c65e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a770609f2de94a7f275ca9aa56bd10d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494bec795f8801911f151ce53b2d4707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
(Ⅱ)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e04fe966866f7ad311adedd93cf25c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee678e1e5ddbaa34b701f64d1e3314d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![]() | ![]() | ![]() | ![]() | ![]() |
![]() | ![]() | ![]() | ![]() | ![]() |
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ab09aee8798546e7eb4b5b9699eac6.png)
(Ⅲ)定义集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f9e136a097820e1adf36afe51837cef.png)
请问:是否存在常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8fd8324d116047aa3f0355ebc0e6671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc2ccaad45af8bfcfcedfeb7149ed5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3029e1dcac54747531d96672f917d238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
11-12高三上·北京东城·期末
5 . 已知集合
中的元素都是正整数,且
,对任意的
,且
,有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4809e8caab317fdff7a4ee3295ca671f.png)
(I)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa3c500d6e62a46f3dccf0099e806f4.png)
(II)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d40709a5e8d31d0dde84226dd12bf47.png)
(III)对于
,试给出一个满足条件的集合A.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c3301017a56b4427b6fab492f63b86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e13a814f8e081078dcf3788177affcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11a069688e4c797fcf527eab15afa82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4809e8caab317fdff7a4ee3295ca671f.png)
(I)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa3c500d6e62a46f3dccf0099e806f4.png)
(II)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d40709a5e8d31d0dde84226dd12bf47.png)
(III)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294250dbd576bff3da0a1456cb9a88a5.png)
您最近一年使用:0次
名校
6 . 已知数列
满足
,
,数列
的前n项和为
,
,其中
.
(1)求
的值;
(2)证明:数列
为等比数列;
(3)是否存在
,使得
若存在,求出所有的n的值;若不存在,请说明理由.
![](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/6d8ca10489eb08b7830922cc9f1b6dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314501f06c7e4bf3112fe41ecac7be68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9d2e152db0845ff23e4ea0cd00974d.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f636df3ea3c910b25ca80b6cad9a2233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e769431b98f3ef867f58353b99784ef.png)
您最近一年使用:0次
2016-12-03更新
|
1741次组卷
|
2卷引用:2015届北京市昌平区高三上学期期末质量抽测理科数学试卷
12-13高三上·安徽安庆·阶段练习
真题
解题方法
7 . 已知
是定义在
上的不恒为零的函数,且对于任意的
,
都满足:
.
(1)求
,
的值;
(2)判断
的奇偶性,并证明你的结论;
(3)若
,
(
),求
的前
项的和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b69d9577de4ee7c342dda447fa7bc8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896df31f80127adbae738b3a014bd4e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c7868f798eced7c48e5186761bfc59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a55e4115c36490a40f83d15f066bd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次