1 . 下列命题正确的有( )个
(1)函数
在
上存在导函数.且
在
上为严格增函数.则
对所有的
恒成立
(2)周期函数
在
上存在导函数,则导函数
也为周期函数
(3)定义在
上的函数
,满足
且
对所有的
恒成立,则
对所有
恒成立
(1)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c72d250a079379c5175693c165248c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
(2)周期函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(3)定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bea8bf593f594c51fc7cc547482bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd75f7cce41d9450f7e885d34231e0cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee4c3872583bef56de103e4a4df05838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
A.3 | B.2 | C.1 | D.0 |
您最近一年使用:0次
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解题方法
2 . 若函数
满足
,则称函数
为延展函数,已知延展函数
和函数
,满足当
时,
,
.给定以下两个命题,则( )
①存在函数
与
有无穷多个交点;
②存在函数
与
有无穷多个交点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87695ff43906838ce161fa0a146d1d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9e8c02924ac2ab7f930e03d96b8fc72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047056c99b39c70fa40d3c8178e5b631.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/428d922e63d8a0838da6fdacee919ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a8cca804253e0975a7976f5615ad20.png)
①存在函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681400804c48154314c35da776022fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
②存在函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681400804c48154314c35da776022fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
A.①真②真 | B.①真②假 | C.①假②真 | D.①假②假 |
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3 . (1)在用“五点法”作出函数
的大致图象的过程中,第一步需要将五个关键点列表,请完成下表:
(2)设实数
且
,求证:
;(可以使用公式:
)
(3)证明:等式
对任意实数
恒成立的充要条件是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/467a953b54798b6e2dcd6d76f8817938.png)
0 | |||||
0 | |||||
1 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d95727eed094e7ceb6663ee9d39bda3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/141ba74bc522b95958aea59cdc8c93d0.png)
(3)证明:等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83576aaf57c7ebdcf56110fdbb0c12a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d8ae1706a9ea5df3eca17eaa5c8b71.png)
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4 . 烧水时,水温随着时间的推移而变化.假设水的初始温度为
,加热后的温度函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a75c767798abfb5dcb88cd21dc4e64c.png)
(
是常数,
表示加热的时间,单位:min),加热到第10min时,水温的瞬时变化率是_________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2969d81e7c1cc013e2bc059ac498f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a75c767798abfb5dcb88cd21dc4e64c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438cf67762709c13f3d15a1a91e8b2c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed3cc507657af0aa845cab1d8bd44d3.png)
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2023-12-23更新
|
965次组卷
|
9卷引用:上海市闵行区七宝中学2024届高三上学期期末数学试题
上海市闵行区七宝中学2024届高三上学期期末数学试题海南省2024届高三上学期一轮复习调研考试(12月联考)数学试题贵州省黔东南苗族侗族自治州2024届高三12月统测(一模)数学试题陕西省西安市长安区教育片区2024届高三上学期模拟考试数学(理)试题(已下线)专题10 导数12种常见考法归类(1)(已下线)第六章:导数及其应用(单元测试)-2023-2024学年高二数学同步精品课堂(人教B版2019选择性必修第三册)(已下线)2.5 简单复合函数的求导法则4种常见考法归类-【帮课堂】2023-2024学年高二数学同步学与练(北师大版2019选择性必修第二册)山东省威海市乳山市银滩高级中学2023-2024学年高二下学期3月月考数学试题福建省泉州市安溪蓝溪中学2023-2024学年高二下学期3月月考数学试题
23-24高二上·上海·课后作业
5 . 已知一罐汽水放入冰箱后的温度x(单位:
)与时间t(单位:h)满足函数关系
.
(1)求
,并解释其实际意义;
(2)已知摄氏度x与华氏度y(单位:
)满足函数关系
,求y关于t的导数,并解释其实际意义.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7fb5d59ac9187a3a401a16bbb9412d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91aecd615d8c0e494cc07848fba49138.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238d537a55326e6018a34043e7e73150.png)
(2)已知摄氏度x与华氏度y(单位:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b1889e56785f45e6dcb4850842a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad64332c9255e7d77e01e187d4c90db.png)
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23-24高二上·上海·课后作业
6 . 吹一个球形的气球时,气球半径
将随空气容量
的增加而增大.
(1)写出气球半径
关于气球内空气容量
的函数表达式;
(2)求
时,气球的瞬时膨胀率(即气球半径关于气球内空气容量的瞬时变化率).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
(1)写出气球半径
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987020b903072c4a667a2c6899b6c4c4.png)
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解题方法
7 . 已知
,记
,
,
.
(1)试将
、
、
中的一个函数表示为另外两个函数复合而成的复合函数;
(2)借助(1)的结果,求函数
的导函数和最小值;
(3)记
,a是实常数,函数
的导函数是
.已知函数
有三个不相同的零点
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/468e12e54a9f92597209394a014926e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d5ede4162743db1282c4c745d5b7c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/117bafde8f721dfd6971cf4e9d2afcbd.png)
(1)试将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
(2)借助(1)的结果,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e00ca9ac35e13b1aa6d614c7a74b471.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07af08f8917a80ef7609df0a89bd6d6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e1fedba462890feb92a798b00314a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e03e21bbdc7f3ae80c1e504863c5294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b24c1b603f987e08cd12944bab0181f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7169ce3255d2a02a20aa5932d2bd48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6c5505a43b336cb503e50975b5341a.png)
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8 . 设
,则满足
在
上恒正的
是__________ .(填写序号)
①
;②
;③
;④
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c765461ae1a6c70f5cbdcb6c932a22b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22add663bd26e87d972a10dc5fd9ada1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89a66279f77b21261b88012a6ac7818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdfb6c182e6983236c9b3af89111dd17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934577743726d3fb09c2dea88430b991.png)
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2023-03-06更新
|
601次组卷
|
5卷引用:上海市2023届高三模拟数学试题
上海市2023届高三模拟数学试题(已下线)核心考点08导数的运算-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)湖南省长沙市师大附中梅溪湖中学(湖南师大附中梅溪湖中学)等2校2023届高三下学期3月联考数学试题甘肃省武威市凉州区2022-2023学年高二下学期期中考试数学试题广东省佛山市禅城实验高级中学2022-2023学年高二下学期3月月考数学试题
9 . 已知定义在
上的函数
(
是自然对数的底数)满足
,且
,删除无穷数列
、
、
、
、
、
中的第
项、第
项、
、第
项、
、
,余下的项按原来顺序组成一个新数列
,记数列
前
项和为
.
(1)求函数
的解析式;
(2)已知数列
的通项公式是
,
,
,求函数
的解析式;
(3)设集合
是实数集
的非空子集,如果正实数
满足:对任意
、
,都有
,设称
为集合
的一个“阈度”;记集合
,试问集合
存在“阈度”吗?若存在,求出集合
“阈度”的取值范围;若不存在,请说明理由;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fee69eaf31dfeb48c691c12384f2d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35679c97cf16aa592343787a756c7c75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8c7bb4fe82c62be38565dae4d303b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce6155e181e21ce56ea658b70f8af17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347bb4ffedcbea2f4c16d047a138d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43f41be870e84c819362787849770519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6db29ed83804b2f681b09cc1b468c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272b44a71d0bec02b3c4f3f05304f942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93205440edb7ad3fe4f13ea76dd29b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65a40142c84be68ee2918c3a8303388c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/971ea1d21d48c4e9a02f633eaada730f.png)
(3)设集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.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/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2470c8ff34402484c137086752eb5e78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54289962af94fdf6270d10e3123ccb1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdbc09b10e4b1a63db906f15469c139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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解题方法
10 . 已知
,
(
)是双曲线
上位于第一象限的任意两点,且
,则函数
的值域为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b225d772013d021cf1bfe7b9421fa5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b7e35faab6d74fa0c36599c39d1698.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1fa37c4c826b5dcfebe86ab6177906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9d6bd79d59276c857eb0e531f1a40a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd1f9ae0ee7f37a1ee021b967db1bfc.png)
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