名校
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“和谐”函数.
(1)判断函数
,
是否是“和谐”函数;(只需写出结论)
(2)设函数
是定义在
上的周期函数,其最小周期为
,若
不是“和谐”函数,求
的最小值.
(3)若函数
是“和谐”函数,求
的取值范围.
![](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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f929c50f8ccc07ba58a4c34bb05d2bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19ec960e7b486de3916696346501a13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b551072bee20e351f14d362a3f0e5367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47431a4b13e3ea3cba79a85fd77eabc2.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1982786864f37e6f954e8d70f9970620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-02-14更新
|
869次组卷
|
3卷引用:2016届北京市海淀区高三上学期期中考试理科数学试卷
名校
2 . 设
满足:
,且
.
(1)求出所有的正整数n,使得
与
平行;
(2)求数列
的前102项的和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08af2c5b79bc1cfdc4eedc85019036ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fcf71cc9796cdd17f4060e18880fb0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7042574fa82069969d5edbf464d9e5e.png)
(1)求出所有的正整数n,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963f817c2da8aceab9a63a783824c65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c14cfccc3cb18eb10a31509c3bf73b0.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5f77fa3bfe60b5fca62bc0c5e8386e.png)
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3 . 设方程
的根是
,方程
的根是
,则
的值是________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbbec3d84599f08226782c7395f8e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba6cc07f6781b34519e7a54c190db7b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
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名校
4 . 已知函数
,且函数
的图象与函数
的图象关于直线
对称.
(1)若存在
,使等式
成立,求实数m的最大值和最小值
(2)若当
时不等式
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6090334f2695f19382eed7425c4f9f44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6461468072bd27afd53fd5f9c3bf344.png)
(1)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2645398c3946e1a9282c219824f167d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9ebfe1a1b9426690757335c2649bb4.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1fdb7ecc0b00a96bdf49f7189342bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7fe88d3778573e668f4530405b29e6e.png)
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2020-01-30更新
|
2657次组卷
|
4卷引用:上海市实验学校2017届高三上学期第三次月考数学试题
名校
解题方法
5 . 已知单位向量
夹角为锐角,对
,
的取值范围是
,若向量
满足
,则
的最小值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ccba3b87a8a48ac3dd5f72d00bdb1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995ec593baa4ef50b6d87c78380953d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859c676e5d3a57b41352d294b450fd68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1480184183ceb2c30e72910f695b578c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d91ef0304f41478fe4309b332e1cd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7b78b446c05c9aea5bf87c7b17258a.png)
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2016-12-04更新
|
1360次组卷
|
2卷引用:2016届浙江稽阳联谊学校高三4月联考数学(文)试卷
名校
6 . 已知
,
.
(1)求当
时,
的值域;
(2)若函数
在
内有且只有一个零点,求
的取值范围.
![](https://img.xkw.com/dksih/QBM/2016/7/4/1572876590702592/1572876597026816/STEM/c20a362c04f54f60b74900b0e0b75a60.png)
![](https://img.xkw.com/dksih/QBM/2016/7/4/1572876590702592/1572876597026816/STEM/ac86192933f0427c8fde067827939a35.png)
(1)求当
![](https://img.xkw.com/dksih/QBM/2016/7/4/1572876590702592/1572876597026816/STEM/56bdb0f61c9443acaca8b191fdcf1e20.png)
![](https://img.xkw.com/dksih/QBM/2016/7/4/1572876590702592/1572876597026816/STEM/e5a1d315894c4809ac77ee28057101d5.png)
(2)若函数
![](https://img.xkw.com/dksih/QBM/2016/7/4/1572876590702592/1572876597026816/STEM/e5a1d315894c4809ac77ee28057101d5.png)
![](https://img.xkw.com/dksih/QBM/2016/7/4/1572876590702592/1572876597026816/STEM/a8d8a732fa3b4aaf9eae8dce77d1b37e.png)
![](https://img.xkw.com/dksih/QBM/2016/7/4/1572876590702592/1572876597026816/STEM/fd9f6b684d034d4f8364769e3b1d1a4c.png)
您最近一年使用:0次
2016-12-04更新
|
3403次组卷
|
2卷引用:2015-2016学年福建省厦门一中高一6月月考数学试卷
7 . 设函数
.
(1)当
时,求函数
的值域;
(2)若
,对任意的实数
函数
恒成立,求实数
的取值范围;
(3)若
,存在实数
使得函数
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0729dcd2c661411f27ed2cc3a89621.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9207fe16acc71001f54c8a10bb13668e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638a1127ac6277a203e7a8c1b035d67c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70df74aa854af3c77bd7386e3e2763d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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