14-15高一上·北京·阶段练习
名校
解题方法
1 . 定义在
上的函数
满足:
对任意
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
恒成立,当
时,
.
(1)求证
在
上是单调递增函数;
(2)已知
,解关于
的不等式
;
(3)若
,且不等式
对任意
恒成立.求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/206e79cb092225550b92d68ae4a18fd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/160daec0ad9ccc242f3e259eb4d61ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adb1dc30d4b297c6d5d0d6d91eab1e3b.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69e5e69fb32ec266ef16839f55e339c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/903e13fa9d0492a446e66783a2b12688.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d6877b6c1eb3eaf7eeaae351116abbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0bcec74eb6f55ad2669157aae8c803.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c32a341bb7f2597378df250b93efdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2016-12-03更新
|
643次组卷
|
3卷引用:2012-2013学年北京二中高一上学期第一次模块考试数学卷
(已下线)2012-2013学年北京二中高一上学期第一次模块考试数学卷辽宁省抚顺市第十中学2016-2017学年高一上学期期中考试数学试题辽宁省抚顺市第十九中学2016-2017学年高一上学期期中考试数学试题
12-13高三上·北京东城·期末
2 . 对于函数
,有如下三个命题:
①
是偶函数;
②
在区间
上是减函数,在区间
上是增函数;
③
在区间
上是增函数;
其中正确命题的序号是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d188aefbf250eb86494d60918164416.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b0328dbb8131d8b24b5f767d1e0a2a4.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bd03a1113a3c036eed26a72e90ec6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2953facaa48d1616c0da2e988bb680.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6a89796c3c24a3d348d97fe1878db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2953facaa48d1616c0da2e988bb680.png)
其中正确命题的序号是
A.①② | B.①③ | C.②③ | D.①②③ |
您最近一年使用:0次
12-13高一上·北京·期末
3 . 函数
的定义域关于原点对称,但不包括数0,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)
,(
是一个正常数);
(3)当
时,
.
证明:(1)
是奇函数;
(2)
是周期函数,并求出其周期;
(3)
在
内为减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.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/dd028447f29935835db4e3aafc54dcd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de175251f4542ac12e81405fc5ad074e.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de175251f4542ac12e81405fc5ad074e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16b8532e1352833824ce93be53d896d6.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb04d514baf56eec084671b88898770b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441145ab6423aa3155c2d56f42ac8883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
证明:(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb3fd46975763046c214db1ed22610b.png)
您最近一年使用:0次
11-12高一上·北京·期中
解题方法
4 . 设函数
的定义域是
,对于任意实数
、
,恒有
,且当
时,
.
(1)若
,求
的值;
(2)求证:
,且当
时,有
;
(3)判断
在
上的单调性,并加以证明.
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b75d15ed45e8112211198215d04629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be4ab7d32ed15c176c550d8543ab369.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51e817f37f5a814e856ebc4a16d676ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffbaf18319364db23f555536976267e9.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eb2613dda00677d447c986cac505bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d752d8db8a05b3ec7312f6ac8b64a07.png)
(3)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
您最近一年使用:0次
11-12高一上·北京·期中
5 . 已知函数
,
.
(1)当
时,判断并证明函数的单调性并求
的最小值;
(2)若对任意
,
都成立,试求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b59dc951a5f0a79b2d3a4ea980a57e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97148e04ca6a9f9dca0aba91ce4e1d84.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97148e04ca6a9f9dca0aba91ce4e1d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
11-12高三上·北京东城·阶段练习
6 . 已知偶函数
在
上为减函数, 且
,则不等式
的解集为________________________ .
![](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/4db7707d6b2754808adefc9b2fb976a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd5e32745ffec9d167aeac9aade85a4e.png)
您最近一年使用:0次
11-12高一上·北京·期中
7 . 设集合
,且
.
(1)求
的值;
(2)求函数
的单调递增区间,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f4415c65041e6bf3be90ca7c1acabfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d2933521158e9e675f2964e8d1fd8d.png)
您最近一年使用:0次
11-12高三上·重庆·阶段练习
名校
8 . 若整数
满足不等式
,则称
为
的“亲密整数”,记作
,即
,已知函数
.给出以下四个命题:
① 函数
是周期函数且其最小正周期为
;
② 函数
的图象关于点
中心对称;
③ 函数
在
上单调递增;
④ 方程
在
上共有
个不相等的实数根.![](https://img.xkw.com/dksih/QBM/2011/10/25/1570330277863424/1570330283237376/STEM/990b9a6e4d694c22b74d1185b53f4c22.png?resizew=12)
其中正确命题的序号是 .(写出所有正确命题的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/622dc9689d99066829e4776270507c62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda2bc2e6a5eaf4fa5ff901985dd0e53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf97282ec523daf6777acb34457a5a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/537297b5e4c881dabdbac8a1db36ce45.png)
① 函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d38feaa3d6708194d17be61f993416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
② 函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d38feaa3d6708194d17be61f993416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abb6b8839973e8a456b5f6ed3c1d586d.png)
③ 函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d38feaa3d6708194d17be61f993416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497199a00f177af4c593e0e715be97f1.png)
④ 方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a1c1dcc6641d2c3cbff44327964eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30a5498bb0236a2bb04ae38329b408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b06e95b57b7a81cd81d05557a11fa92.png)
![](https://img.xkw.com/dksih/QBM/2011/10/25/1570330277863424/1570330283237376/STEM/990b9a6e4d694c22b74d1185b53f4c22.png?resizew=12)
其中正确命题的序号是 .(写出所有正确命题的序号).
您最近一年使用:0次
10-11高二下·北京·期末
9 . 已知
是定义在
上的奇函数,且
,若
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d476f14a11d6a5aae028fe1d4b52c7.png)
(1)用定义证明:
在
上是增函数;
(2)解不等式
;
(3)若
对所有
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249a976e88133f3b3733f09137cf5c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f989f394645ef2f0c856e0adcd333593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d476f14a11d6a5aae028fe1d4b52c7.png)
(1)用定义证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d188ec2580e273ce87e51653a2177ee.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b63adedc645ec99e52a2afb25b6ff21e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0519eee9b07f424d5682622512611fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca579006427f1022e7ca3c49b44c41d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次