名校
解题方法
1 . 已知函数
.
(1)当
时,直接写出
的单调区间(不要求证明),并求出
的值域;
(2)设函数
,若对任意
,总有
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14b2d3738f56987d159a343dc160f384.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cbeede118c407a800b05757b9a1393e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdabdbbbde9b3ee68df66171b0145785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3d5a5e70f64f0933ae1e4ddec5fa2c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61761abb364ece2281af24d9b1f008de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2024-03-07更新
|
516次组卷
|
11卷引用:安徽省合肥市一中、六中、八中三校2020-2021学年高一上学期期末数学试题
安徽省合肥市一中、六中、八中三校2020-2021学年高一上学期期末数学试题安徽省合肥一中、六中、八中2020-2021学年高一上学期期末联考数学试题安徽省淮南市寿县第一中学2020-2021学年高一下学期入学考试数学试题安徽省淮北市树人高级中学2020-2021学年高一下学期开学考试数学试题(已下线)大题好拿分期中考前必做30题(压轴版)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)(已下线)第7章 三角函数 单元测试(单元综合检测)(难点)(单元培优)-2021-2022学年高一数学课后培优练(苏教版2019必修第一册)(已下线)7.3 三角函数的图像和性质(难点)(课堂培优)-2021-2022学年高一数学课后培优练(苏教版2019必修第一册)山东省淄博市美达菲双语高级中学2022-2023学年高一下学期3月月考数学试题湖南省株洲市第二中学2022届高三下学期期中数学试题(已下线)专题17 三角值域问题四川省德阳市德阳中学校2023-2024学年高一下学期入学考试数学试卷
名校
解题方法
2 . 已知
,其中
.
(1)当
,
时,
①任意写出
的一条对称轴;
②求证:
;
(2)若对任意
,
,求
所能取到的最小值和最大值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aba354888ba7e2065e85656c20f31005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360ff131c51a4ef6745538c18cec92c2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191d9381c4f252fbb5553ba72462d0aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5805d32dc3582d0a706c015875c15eb9.png)
①任意写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
您最近一年使用:0次
名校
解题方法
3 . 设
,函数
,
.
(1)讨论函数
的零点个数;
(2)若函数
有两个零点
,
,试证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b30db1d4f4a2cf9b2e7c0224468b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5c9dd749202f50f605cc804bedbe1f.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/c571dcdb66f1c91cea2a9e889da3622d.png)
您最近一年使用:0次
2024-01-29更新
|
699次组卷
|
5卷引用:浙江省杭州第二中学2023-2024学年高一上学期期末数学试题
浙江省杭州第二中学2023-2024学年高一上学期期末数学试题重庆市缙云教育联盟2024届高三下学期2月月度质量检测数学试题湖南省株洲市二中2023-2024学年高一下学期开学考试数学试卷2023新东方高一上期末考数学01(已下线)专题02三角函数的图像与性质期末10种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)
名校
解题方法
4 . 已知函数
.
(1)求证:
;
(2)求函数
的极值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60abf4b672333594a51bb16e3241459.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0779ecedd676e010429ce8a872005c5f.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2023-09-24更新
|
458次组卷
|
3卷引用:湖南省天壹名校联盟2023-2024学年高三上学期9月大联考数学试题
名校
5 . 对于函数
,
,
,
及实数m,若存在
,
,使得
,则称函数
与
具有“m关联”性质.
(1)分别判断下列两组函数是否具有“2关联”性质,直接写出结论;
①
,
;
,
;
②
,
;
,
;
(2)若
与
具有“m关联”性质,求m的取值范围;
(3)已知
,
为定义在R上的奇函数,且满足:
①在
上,当且仅当
时,
取得最大值1;
②对任意
,有
.
求证:
与
不具有“4关联”性质.
![](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/4413796ac3d5ca067bf70334101f5440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3ac1b540727626af78788a8e5f15de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe6b84f7980bf119ee652fc253ed759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)分别判断下列两组函数是否具有“2关联”性质,直接写出结论;
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a18ca67c2770b98f36dbfd802595a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ba296251f96be272abf30c1c0e1a8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1591d4244dcf5539a4ae98f554e91e61.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699f767ccf837c2bf8019d03451849c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/636289ad84b4a3a51095dd32ca201f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/174550b7c81d8d41084dcafad90bfbe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a79d7f73b6128650bf7aed538260c72.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96101eb5dce02c0213ad008413f3066.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57a78355986534b6e50bd7cabc9290a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede97915bccd6a7b22d7400c30f8adea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18db64040b2fa9d65075b41ada928fa6.png)
求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9c839f85fe048ed0882889e22f5166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d2c5422d4b9f8c11a5ad1b62c6bb87.png)
您最近一年使用:0次
2023-06-19更新
|
339次组卷
|
3卷引用:北京市顺义区2022-2023学年高一下学期期中考试数学试题
名校
6 . 设函数
定义域为D,对于区间
,如果存在
,使得
,则称区间I为函数
的“P区间”.
(1)求证:
是函数
的“P区间”;
(2)判断
是否是函数
的“P区间”,并说明理由;
(3)设
为正实数,若
是函数
的“P区间”,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31b14d5b4da0298a7dea660b03d1066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d71122e87403561adbcdac88945c481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2698a5500308daa68bc4c38d5caab41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f0fadbe551b0e0eb7bf9440be740b9.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a19bbab2270fc8e694527e801556cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6989274f11bf66835d5d4f82bce7f7.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65713c48e9847b892424ceee83b134f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894b6be92b8cefcb58ab237211fef088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
您最近一年使用:0次
名校
7 . 已知
,
.
(1)若
,求
的取值范围;
(2)若函数
恰有两个零点,求实数a的取值范围;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b39c5d66018f0736a0457961c91e1c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17a1141aa62d95fc3b75e3d6833aaaf0.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98a3f237b03aaa5f0fb96e572706349c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732a3c49d8680218bdcc2f39f2b4f601.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08180ea9d4238fd449255a0b47f3bb2f.png)
您最近一年使用:0次
8 . 已知函数
有两个零点.
(1)求实数a的取值范围;
(2)设
,
是g(x)的两个零点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb1e47f447e170fa22a57cceb954de6.png)
(1)求实数a的取值范围;
(2)设
![](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/c07bbaa783c21744c573ce71de07b92a.png)
您最近一年使用:0次
2023-07-09更新
|
1310次组卷
|
9卷引用:河南省洛阳市2022-2023学年高一下学期期末数学试题
河南省洛阳市2022-2023学年高一下学期期末数学试题(已下线)第1课时 课后 函数的零点浙江省名校协作体2023-2024学年高二上学期开学适应性考试数学试题(已下线)第四章 三角函数与解三角形 第四节 第二课时 三角函数的图象与性质(二)(B素养提升卷)(已下线)第五章 三角函数(压轴题专练)-速记·巧练(人教A版2019必修第一册)(已下线)模块二 专题4《三角函数的图像和性质》单元检测篇 B提升卷 (人教A)广东省中山市2023-2024学年高一上学期期末数学试题(已下线)模块一专题3《三角函数的图像和性质》单元检测篇B提升卷(人教B)(已下线)模块一 专题2《三角函数的图像和性质》单元检测篇B提升卷(北师大版高一期中)
9 . 对
,定义
.
(1)求
的最小值;
(2)
,有
恒成立,求A的最大值;
(3)求证:不存在
,且m>n,使得
为恒定常数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97769855336d73371930df1f187875e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f166b8917034ebc7522d1a160707f6a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7de87e4f04e15189c927b34b2e5afb.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bde2576b383ae3c851529435805b3adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b206982b923b94befb9985e51f6499cb.png)
(3)求证:不存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c61a450b5c1c412aca3294e9eb4e9874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c29ca729804f56f23d760ab66b79f68.png)
您最近一年使用:0次
2021-07-19更新
|
544次组卷
|
3卷引用:北京市一零一中学2020-2021学年高一下学期期末数学试题
10 . 对于函数
,若存在正常数
,使得对任意的
,都有
成立,我们称函数
为“
同比不减函数”.
(1)求证:对任意正常数
,
都不是“
同比不减函数”;
(2)若函数
是“
同比不减函数”,求
的取值范围;
(3)已知函数
是定义在R上的奇函数,当
时,
.是否存在正常数
,使得对于任意的
,函数
都为“
同比不减函数”,若存在,求
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9298ea50c497b0ad0905c08d72565892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4c64c9f7e6d921f2f134b832dc87e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)求证:对任意正常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3e9c31b39b443a4ac19740ba7dece6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5e5727d78c170a69fade80116d645f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a111628c5ea54305dba24105b84900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
您最近一年使用:0次