1 . 定义函数
,其中,
,
.
(Ⅰ)设函数
,求
的定义域;
(Ⅱ)设函数
的图像为曲线
,若存在实数
使得曲线
在![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
处有斜率为
的切线,求实数
的取值范围;
(Ⅲ)当
且
时,试比较
与
的大小(只写出结论).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992420d8a38c98a9815d7af8bd91efd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7fde71807463dbdfd8fce1655a5a9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df5448211fb91c57a2bb7298c54cc49.png)
(Ⅰ)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d632f82cf3b911747d11c15767f00366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03bf4bae5a46b470fdfcbb84f8e115eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78e690a20c64a6c7c85467445101233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d6e7588896b9fcf88d26caeba8bfc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(Ⅲ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9f23e77cfb325e56a17d6960768c932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf59f62d3f838fbc226c6e7c229e3c1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5006b7b4c0de541795eb5597e0e7a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388f4c4c4bbd00e4be744ddcd057ad2d.png)
您最近一年使用:0次
2 . 某地实行阶梯电价,以日历年(每年1月1日至12月31日)为周期执行居民阶梯电价,即:一户居民用户全年不超过2880度(1度=千瓦时)的电量,执行第一档电价标准,每度电0.4883元;全年超过2880度至4800度之间的电量,执行第二档电价标准,每度电0.5383元;全年超过4800度以上的电量,执行第三档电价标准,每度电0.7883元.下面是关于阶梯电价的图形表示,其中正确的有
![](https://img.xkw.com/dksih/QBM/2016/3/4/1572518713155584/1572518718750720/STEM/f655ed09d6ab4a29808d0f14f841b84f.png)
参考数据:0.4883元/度
2880度=1406.30元,
0.5383元/度
(4800-2880)度+1406.30元=2439.84元.
![](https://img.xkw.com/dksih/QBM/2016/3/4/1572518713155584/1572518718750720/STEM/f655ed09d6ab4a29808d0f14f841b84f.png)
参考数据:0.4883元/度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04490c62035e93ac5446d2d017facc41.png)
0.5383元/度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04490c62035e93ac5446d2d017facc41.png)
A.①② | B.②③ | C.①③ | D.①②③ |
您最近一年使用:0次
2016-03-04更新
|
511次组卷
|
4卷引用:2016届北京市丰台区高三上学期期末联考文科数学试卷
2016届北京市丰台区高三上学期期末联考文科数学试卷2016届宁夏·海南高三三轮冲刺猜三文科数学试卷2016届高三(亮剑·快乐考生)三轮冲刺猜题(三)文数试卷(已下线)《2018-2019学年同步单元双基双测AB卷》必修一 专题八 函数模型与应用 A卷
12-13高一上·北京·期末
解题方法
3 . 函数
的定义域关于原点对称,但不包括数
,对定义域中的任意实数
,在定义域中存在
使
,且满足以下3个条件.
(1)
是
定义域中的数,
,则
;
(2)
是一个正的常数);
(3)当
时,
.
证明:(I)
是奇函数;
(II)
是周期函数,并求出其周期;
(III)
在
内为减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0aff4b41805fecb8ddc7f6990d9a10c.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f27822887caad20f3a075ca2fb74155c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095be928748d6aee0cae4e9f69981f9e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a606c7099a87a8403c9c8c905d1bff4.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441145ab6423aa3155c2d56f42ac8883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
证明:(I)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(II)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(III)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/682f449e32b92543daf6c08bfefdcb9c.png)
您最近一年使用:0次
名校
4 . 已知函数
是定义域为
的偶函数,当
时,
,若关于
的方程
,有且仅有6个不同实数根,则实数
的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbf0626e7ca241e06a108f351c26e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e1aa2c72251ba7eae4890b4f39619c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2015-09-16更新
|
1363次组卷
|
5卷引用:【全国百强校】北京师范大学附属中学2018-2019学年高一上学期期末考试数学试题
5 . 已知集合
,其中
,由
中的元素构成两个相应的集合:
,
.
其中
是有序数对,集合
和
中的元素个数分别为
和
.
若对于任意的
,总有
,则称集合
具有性质
.
(Ⅰ)检验集合
与
是否具有性质
并对其中具有性质
的集合,写出相应的集合
和
.
(Ⅱ)对任何具有性质
的集合
,证明
.
(Ⅲ)判断
和
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8213c48030bc2cfa88da0f2a28aca2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d807832357bea22a266e63cbd7e678a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976ed3659749e70adb41abe4030b6ef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/604a1abd24826ba48fe69d714b1b16d0.png)
其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
若对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2cacc52ffe015e828a4a5f2fe5ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(Ⅰ)检验集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e565001c699e5e221ed616dd7be2bb83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0110544a65399ad66980adc3667b8b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(Ⅱ)对任何具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca7597aeef0ed7313f6f78b9658ea5e.png)
(Ⅲ)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
2016-11-30更新
|
3435次组卷
|
11卷引用:2007年普通高等学校招生全国统一考试理科数学卷(北京)
2007年普通高等学校招生全国统一考试理科数学卷(北京)北京东城27中学2018届高三上学期期中考试数学试题北师大附中2017-2018学年高一下学期期末数学试题1北师大附中2017-2018学年高一下学期期末数学试题22007 年普通高等学校招生考试数学(理)试题(北京卷)上海市大同中学2018-2019学年高一上学期10月学情调研数学试题北京市第二中学2021届高三高考模拟数学试题北京市第十三中学2022届高三上学期开学考数学试题北京市朝阳区北京中学2022-2023学年高一上学期期中数学试题上海市复兴高级中学2021-2022学年高一上学期10月月考数学试题北京名校2023届高三二轮复习 专题三 集合与数列 第3讲 集合与数列创新题