名校
解题方法
1 . 已知函数
,
.
(1)若函数
在R上单调递减,求a的取值范围;
(2)已知
,
,
,
,求证:
;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d013335d41c7a1e51b381eb8e7ef977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111870a9ef48f1bb2797ae8f1825a8f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9897559d21ef1971f497be4269b107aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0527a896aec4a245945e5edee00deed.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f6bf190c55c3a0ddbca2ff7a5ecf42.png)
您最近一年使用:0次
2023-12-30更新
|
1121次组卷
|
4卷引用:吉林省通化市梅河口市第五中学2023-2024学年高二下学期第一次月考数学试题
吉林省通化市梅河口市第五中学2023-2024学年高二下学期第一次月考数学试题陕西省名校协作体2024届高三上学期一轮复习联考(四)数学(文)试题(已下线)专题2-6 导数大题证明不等式归类-1(已下线)导数及其应用-综合测试卷A卷
解题方法
2 . 对于函数
,
和
,
,设
,若
,
,且
,皆有
成立,则称函数
与
“具有性质
”.
(1)判断函数
,
与
是否“具有性质
”,并说明理由;
(2)若函数
,
与
“具有性质
”,求
的取值范围;
(3)若函数
与
“具有性质
”,且函数
在区间
上存在两个零点
,
,求证
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02059edf02fba0e7c62b7c2a48ef1184.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bed7a0e7e7a3b49b4cd2e777a64e9061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a573996f5d4b27434a4491928b59f301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e450d0e48276909b7387fb576df4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93815f534a9ba003799aef2a53a242.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53224898de85a85058ad336490bbbaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49636685bca80ed0864d65d829973f8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/798548b5fbb631a0828621581a741f06.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a151adfdf0446b1ac074bca90076df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaae91ed6da60e86e3bb9b3eb7e03e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba0154a5c65b0b304c7e4df2e738f78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e93815f534a9ba003799aef2a53a242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb8ca1f5da558af68ebe76d985dbbe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b96ee0875a6bcaf9371fb9cfd7eae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04133adb6f1562d859510c9771b2e545.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
是定义在
上的奇函数.
(1)求实数
的值;
(2)判断
在定义域上的单调性,并用单调性定义证明;
(3)
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13cbc2ed4bad6431037602fc427e6756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5667bc1ea875422f618529aa5f254f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e9b1365d76a10c212db1c91c5f91f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
4 . 已知函数
在定义域
上为偶函数,并且函数
.
(1)判断
的奇偶性,并证明你的结论;
(2)设
,若对任意的
,总存在
,使得
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152043781d916de477d7611cb683a67b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c379c978805211415624917ef4c2c97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/494ca37214184b7f655c7810851d3b72.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8336841b5bc3cb4913835080b9d85933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f9d255ca420fa2486b11fcb7763b44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204e6006eacca1a448fe6991f3c121f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45bc85e19745af6992cbb72c3fd79ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
您最近一年使用:0次
名校
解题方法
5 . 设函数
.
(1)判断函数
在区间
和
上的单调性(不需要证明过程);
(2)若函数
在其定义域内为奇函数,求
与
的关系式;
(3)在(2)的条件下,当
时,不等式
在
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb700a41926e88302e5c1a272ec1bdd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)在(2)的条件下,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a60372066c996c42b5cbf82e1bbefab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
6 . 已知
是定义在
上的函数,如果存在常数
,使得对区间
的任意划分:
,都有
成立,则称
是
上的“绝对差有界函数”.
(1)分别判断
,
是否是
上的“绝对差有界函数”,若是“绝对差有界函数”,直接写出
的最小值(不需证明);若不是“绝对差有界函数”,直接写出函数的值域(不需证明);
(2)对定义在
上的
,若存在常数
,使得对任意的
,都有
,求证:
是
上的“绝对差有界函数”;
(3)设
是
上的“绝对差有界函数”,满足
,
,且对任意的
,都有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804319e6cb58f07ee82ee364e334f36b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cddd157e5a81d11a17daeae7882b85f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
(1)分别判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee02fa2349fe9b9dd17c11665352c06e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a552e0f8ccb78f2eec126ba95d8c399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)对定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f20b947d584a1dc48676c2ae6e2af52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ecdccf4a334ea959a456533c40d53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ac1c23f2a39df0652588ce63221df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd80e859f2a7935d7d621e202422621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
7 . 函数
的定义域为D,若存在正实数k,对任意的
,总有
,则称函数
具有性质
.
(1)判断下列函数是否具有性质
,并说明理由;
①
;
②
;
(2)已知
为二次函数,若存在正实数k,使得函数
具有性质
.求证:
是偶函数;
(3)已知
,k为给定的正实数,若函数
具有性质
.求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a380348dd1544f954255976659a84a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
(1)判断下列函数是否具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2387880727d458702651d699e76d7d76.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5bc39061e1fb75d8ab1fd5c3765a514.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4306fb6d5419322b4b7b9140e06e43a0.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88a63bbc4eadab1cbce4dbfaf8d411.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daac43c7675fa411b35028e09b0bad90.png)
您最近一年使用:0次
2023-11-24更新
|
237次组卷
|
2卷引用:湖南省长沙市周南中学2022-2023学年高二上学期暑假学习评价检测数学试题
名校
8 . 如图,在四棱锥
中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234205f80829a5bbc6ae3a675fe4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28155ab6f06636cae7e5a4eb07e580d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836ac3d625647007c99532bac34a6f92.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a8911f5302c0a65c1d28c0ed1c939e.png)
为
的中点.
平面
;
(2)求平面
与平面
的夹角的余弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2234205f80829a5bbc6ae3a675fe4f85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28155ab6f06636cae7e5a4eb07e580d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/836ac3d625647007c99532bac34a6f92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d618f2f945043c0fc4b2bb492206d4cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a8911f5302c0a65c1d28c0ed1c939e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d781525777c7b5284dffc70b2a28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
名校
解题方法
9 . 已知
,函数
.
(1)若对
,
恒成立,求a的取值范围;
(2)若
在点
处的切线为
,
与x轴的交点为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad17ed095d590d7419e7ba54f3302ea6.png)
(1)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526e32d92b402faa5689139dec4e4915.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27c0ab3e2d7698f082854bafe4174dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad69338c7ddd466a46e864604be2d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14d8ea86980c657735bf928b627d6db.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数
为奇函数.
(1)求
,判断
的单调性,并用定义证明;
(2)若不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ca09548bb2ade976e4db708ff209c4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2a56a3dbc9d402e33f172d90694b44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2024-02-18更新
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4卷引用:辽宁省名校联盟2023-2024学年高二下学期4月联合考试数学试卷