名校
解题方法
1 . 已知数列
中
,关于
的函数
有唯一零点,记
.
(1)判断函数
的奇偶性并证明;
(2)求
;
(3)求证:
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f4d4fa1b049045d58a9571a0709004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/072010cccaa77474c07b66816ce4ae92.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f4d4fa1b049045d58a9571a0709004.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f8c399c162dbd37d2aa304a4a3a1fd.png)
您最近一年使用:0次
名校
解题方法
2 . 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
|
513次组卷
|
11卷引用: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(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
名校
解题方法
3 . 已知函数
的定义域为
,若对于给定的非零实数
,存在
使得
成立,则称函数
具有性质
.
(1)已知
,判断函数
是否具有性质
,并说明理由;
(2)已知
,若函数
,
具有性质
,求正实数
的取值范围;
(3)已知函数
,
的图像是连续不断的曲线,且
,求证:函数
,
具有性质
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca2452e9315b65152f13e0b85edab77a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834925e383a1e904951eea76b55bcb4f.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d9459134e886dc7fb76a0221dbadb1.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1044dcf4fba551e1b7fbfeb895ea08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b874e45974ce6a77f78f561406d779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65f2f580fa5ab9f36897306bb05a306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9c518d889fe12a5d73ad829bb36e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf5f2b93641d1f16b86d3c1fd398ab7f.png)
您最近一年使用:0次
名校
4 . 有如下条件:
①对
,
,2,
,均有
;
②对
,
,2,
,均有
;
③对
,
,2,3,
;若
,则均有
;
④对
,
,2,3,
;若
,则均有
.
(1)设函数
,
,请写出该函数满足的所有条件序号,并充分说明理由;
(2)设
,比较函数
,
,
值的大小,并说明理由;
(3)设函数
,满足条件②,求证:
的最大值
.(注:导数法不予计分)
①对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33de1fa20e0bb8fa1d5a4f4bfc471139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2f24b4fa5308650a244d954f78f09b.png)
②对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33de1fa20e0bb8fa1d5a4f4bfc471139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca3ecbbaca8eeb1cfa8f4035f7d5726.png)
③对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33de1fa20e0bb8fa1d5a4f4bfc471139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c8f1c6b5fa1bd63ca493856b8e600b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5141a62d81c04d7c20f4135cc7f1dbb.png)
④对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33de1fa20e0bb8fa1d5a4f4bfc471139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c8f1c6b5fa1bd63ca493856b8e600b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa8e4c6783752d1090385ff08a9f7a7.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38724fa88a08e6b45a5eb248ca8807b9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1c7571006978c5115a9a6bd764698a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ed4309f300802aef509cf52bd754ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da281ccca7c32c2052b29c83383fcc5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb71a578b8da093174f94e14fe4cb4bb.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbbdd006d6c6aa4c00282f564718a03a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db7f4871ab297375b0e1598479164f5.png)
您最近一年使用:0次
2024-02-23更新
|
510次组卷
|
5卷引用:福建省部分优质高中2023-2024学年高一下学期入学质量抽测数学试卷
名校
解题方法
5 . 设函数
,
,
.
(1)求函数
在
上的单调区间;
(2)若
,
,使
成立,求实数a的取值范围;
(3)求证:函数
在
上有且只有一个零点
,并求
(
表示不超过x的最大整数,如
,
).
参考数据:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89231f0078f75ad0193f9aec97b9286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa3e40a1b375c50331403283bfd7139b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0167434c2c1a16e59e89d436ac0a1278.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69fc78bba43797d2f81cb912f2d05c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac0afd127806b03435a649606544fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe53bb5e833f83c2d8290d195fabf02b.png)
(3)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b5e51f08fcfaa95b58f3a14c8250a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41667e2986ec718cabeeb1088794ed67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04309e875209bde5b87438535ea3b1cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/977353e0326dc27334a2940f1149e973.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dad09268b7cb8bfcbea010cb6d2a29e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e143d31a5ae4d2fb8cba2466bae1fe54.png)
您最近一年使用:0次
2024-01-06更新
|
656次组卷
|
6卷引用:福建省部分优质高中2023-2024学年高一下学期入学质量抽测数学试卷
名校
6 . 如果函数
的导数
,可记为
.若
,则
表示曲线
,直线
以及
轴围成的“曲边梯形”的面积.
(1)若
,且
,求
;
(2)已知
,证明:
,并解释其几何意义;
(3)证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d4d758bac9a7272c1d40a5ea4176c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edd8f5b33be6db5be0833f1801bd7a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c6a5e6776e205fb09d8a689e1638947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436ff3cf58de28b55f7605675a47d818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8ed0afb829f4d5c61ce89a556376d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0dc2a031743126b8b4fabb843a55bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bc282dae4ac9132196ac5d13f63b901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c38abf9dbef1c45d9fd8143798fa0ea.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59176a49cf2e21c94cf550888de88c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
您最近一年使用:0次
2024-02-20更新
|
2423次组卷
|
7卷引用:重庆市第八中学校2023-2024学年高三下学期入学适应性考试数学试题
重庆市第八中学校2023-2024学年高三下学期入学适应性考试数学试题(已下线)压轴题函数与导数新定义题(九省联考第19题模式)练(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编湖北省十一校2024届高三联考考后提升数学模拟训练一湖北省黄冈市浠水县第一中学2024届高三下学期第三次高考模拟数学试题(已下线)第5套 新高考全真模拟卷(二模重组)(已下线)压轴题01集合新定义、函数与导数13题型汇总-2
名校
解题方法
7 . 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
|
684次组卷
|
5卷引用: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
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)
8 . 已知
,
为锐角,求证:“
”是“
”成立的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0880c9ff556d06c0b07b4df2ff326b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f179960d3b309a204f01222d8069f2.png)
您最近一年使用:0次
解题方法
9 . 如图,在正方体
中.
(1)求异面直线AC与
所成角的大小;
(2)求证:
;
(3)求二面角
平面角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/9/f7cc5cc1-0f28-42fb-b836-d741671c1fc6.png?resizew=152)
(1)求异面直线AC与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a0e00113872f921116b6c0c3177d0f.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec99f21b5368bf8776e62003c12dd705.png)
您最近一年使用:0次
2023-08-09更新
|
437次组卷
|
2卷引用:新疆阿拉山口市中学2023-2024学年高二上学期开学考试数学试题
名校
解题方法
10 . 在四棱锥
中,底面
是梯形,
,
,
,侧棱
.
(1)证明:平面
平面
;
(2)若
,
是
的中点,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e52411c8437d0640c5b3d87cf5ebebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12143a06ed24558d8cc7ad39961d3e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30fc65a72853bd8ac1ad0828270d3baf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/a8957195-8540-4200-9b17-722531d36b0d.png?resizew=157)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace900749d0861aa51fcc6d72c51f82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cfa5b176fd1316fb676bbee21cc5f02.png)
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