名校
1 . 对
,
,若
,使得
,都有
,则称
在
上相对于
满足“
-利普希兹”条件,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f2eef0405a16a192a197055723ccd9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa875bb5463d3f0046aa91bd596c440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/510d5cb049af38d5c4fed742281aebad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2836e6fab597cbfbbc38ce832c6d0191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d484eaef6688f8014442e658edf6f6a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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9卷引用:重庆市南开中学2022-2023学年高一上学期12月月考数学试题
重庆市南开中学2022-2023学年高一上学期12月月考数学试题浙江省宁波市九校2021-2022学年高一上学期期末联考数学试题浙江省杭州市富阳区江南中学2021-2022学年高一下学期开学考试数学试题浙江省温州市乐清市知临中学2022-2023学年高一上学期11月期中数学试题湖北省武汉市2021-2022学年高一上学期期末模拟数学试题(一)湖北省武汉市华中师范大学第一附属中学2022-2023学年高一上学期期末模拟数学试题(三)四川省南充高级中学2022-2023学年高一上学期期末数学试题第4章 指数概念与对数函数(基础、典型、易错、新文化、压轴)专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)(已下线)必修第一册综合检测-人教A版(2019)必修第一册单元测试能力卷
名校
2 . 若对任意的实数
,都存在以
,
,
为三边长的三角形,则正实数
的可能取值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a63e5b24f4659539f4c6e8d426f263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f123b414c4004893fc3b7bcc774711.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
A.![]() | B.1 | C.![]() | D.2 |
您最近一年使用:0次
名校
解题方法
3 . 对于两个函数:
和
,
的最大值为M,若存在最小的正整数k,使得
恒成立,则称
是
的“k阶上界函数”.
(1)若
,
是
的“k阶上界函数”.求k的值;
(2)已知
,设
,
,
.
(i)求
的最小值和最大值;
(ii)求证:
是
的“2阶上界函数”.
![](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/3d6afd1b3aeae1bd415dba90e50c001c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffea0f7bb26c02be91008a3a992a27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5289677c3bf66194c475c4c44f4a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06f45220c23094a3d9ef53b54b89d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2bc8d66faac1a06acfec68e28086bf.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b89d55ca6a541bce15e141a7e38285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f0ca536621ec8db02707ba65917029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ff2689759a35f3a8030b02be7a22c3.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e49794721f5504dd828acf49be37ff42.png)
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2022-01-24更新
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1591次组卷
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2卷引用:重庆市巴蜀中学2021-2022学年高一上学期期末数学试题
名校
解题方法
4 . 如图,圆柱
的轴截面ABCD为正方形,
,EF是圆柱上异于AD,BC的母线,P,Q分别为线段BF,ED上的点.
![](https://img.xkw.com/dksih/QBM/2022/4/23/2964375380615168/2965847181041664/STEM/3e77eb85-a8cb-4d19-a8b9-ba53f2b5fdb7.png?resizew=186)
(1)若P,Q分别为BF,ED的中点,证明:
平面CDF;
(2)若
,求图中所示多面体FDQPC的体积V的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/2022/4/23/2964375380615168/2965847181041664/STEM/3e77eb85-a8cb-4d19-a8b9-ba53f2b5fdb7.png?resizew=186)
(1)若P,Q分别为BF,ED的中点,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72221ee5b504d596ff799c0b356aa0ea.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4996f88b6be9b1df67f43771eda6d36f.png)
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2022-04-25更新
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1601次组卷
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5卷引用:重庆市南开中学校2021-2022学年高一下学期期中数学试题
重庆市南开中学校2021-2022学年高一下学期期中数学试题重庆市南岸南坪中学校2022-2023学年高一下学期期中数学试题(已下线)第02讲 玩转立体几何中的角度、体积、距离问题-2022年暑假高一升高二数学衔接知识自学讲义(人教A版2019)辽宁省大连市第八中学2021-2022学年高一下学期6月月考数学试题吉林省延边朝鲜族自治州延吉市延边第二中学2022-2023学年高一下学期期中数学试题
名校
解题方法
5 . 意大利著名画家、数学家、物理学家达·芬奇在他创作《抱银貂的女子》时思考过这样一个问题:固定项链的两端,使其在重力的作用下自然下垂,那么项链所形成的曲线是什么?这就是著名的悬链线问题,连接重庆和湖南的世界第一悬索桥——矮寨大桥就采用了这种方式设计.经过计算,悬链线的函数方程为
,并称其为双曲余弦函数.若
对
恒成立,则实数
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7724a609e7f2f7a23723727dd5850cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cc07a310483493cc09c6473d3538e41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7625638e37a8223ff0ed057a4ae0349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/6a7122bd-d25a-49ba-af45-75d661d35049.png?resizew=300)
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1352次组卷
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5卷引用:重庆市南开中学2021-2022学年高一上学期期末数学试题
重庆市南开中学2021-2022学年高一上学期期末数学试题(已下线)第02讲 二倍角的三角函数-【帮课堂】2021-2022学年高一数学同步精品讲义(苏教版2019必修第二册)重庆市长寿中学校2023届高三上学期期中数学试题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(已下线)高一上学期期末【压轴60题考点专练】-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)
名校
6 . 若在函数
的定义域内存在区间
,使得
在
上单调,且函数值的取值范围是
(
是常数),则称函数
具有性质
.
(1)当
时,函数
否具有性质
?若具有,求出
,
;若不具有,说明理由;
(2)若定义在
上的函数
具有性质
,求
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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad8af7bed124f00c8e19b52d028b4d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8493a0cd10d3d0399173c04163740a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec84404bbf6cf4a9d992e1760dcfdd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023de14f801222173f4ff30850c87626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-02-21更新
|
587次组卷
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3卷引用:重庆市第八中学校2023-2024学年高一上学期期中数学试题
名校
解题方法
7 . 2022年北京冬奥会期间,小明对火炬(图22-1)产生了浓厚的兴趣,于是准备动手制作一个简易火炬(图22-2).通过思考,小明初步设计了一个平面图,如图22-3所示,其中
为直角梯形,且
,
,
,
,
,曲线
是以C为圆心的四分之一圆弧,
为直角三角形,
,将平面图形
以
所在直线为轴,旋转一周形成的几何体即为小明设计的简易火炬.
(1)求该简易火炬的体积;
(2)小明准备将矩形
(如图22-3所示,该矩形内接于图形
,M在弧
上,N在线段
上,
与
重合)旋转所形成的几何体都用来安放燃料,设
,
①请用
表示燃料的体积V;
②若火炬燃烧时间t和燃料体积V满足关系
,请计算这个简易火炬燃烧的最长时间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b312dab930cbbb9a4bb1a99f044dab73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27ec6fb9b50ec0d739a2bbe317fe2d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2bd00552faa7dcdbda8aaf1f7b5bf29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0761165f1176f3a5fe4f7b052832316d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5be03b66d8e48af54e5bb366818c389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27718c7561d646d66db48e330332471c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d483a2ea171d8c7a6b9ac303c8114ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecc1cb55a57dde481f8dd07ab150676.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/23/6aaf3b25-5421-4a1a-b2f4-fe069411ded0.png?resizew=293)
(1)求该简易火炬的体积;
(2)小明准备将矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec780e86f57790cf88ec761e219bf5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5942a3d31a263325ad5a68cdaa02d1ed.png)
①请用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
②若火炬燃烧时间t和燃料体积V满足关系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea8712e7c38f0d3d8ad16af60dc46f77.png)
您最近一年使用:0次
名校
8 . 如图所示,等腰梯形
中,
,
,已知E,F分别为线段
,
上的动点(E,F可与线段的端点重合),且满足
,
.
关于x,y的关系式并确定x,y的取值范围;
(2)若
,判断是否存在恰当的x和y使得
取得最大值?若存在,求出该最大值及对应的x和y;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e921f46d90e43f4517c55832b6280f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c3f33f58f50ec2d5f038e620c3294f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1578eb173c8b9a7a124c988f77a690bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14c37cb57db83fb57e6a0d3a0afa1127.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a5df115177284576970a912b09ba7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916bb2cc1b29574ff95b47567c59ee0c.png)
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2022-04-03更新
|
1179次组卷
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8卷引用:重庆市开州中学2021-2022学年高一下学期第一次阶段性考试数学试题
名校
解题方法
9 . 已知函数
的定义域为
,
,满足
,
,令
,设当
时,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea944fa5b7030c92f0d06e7e15c1c135.png)
(1)计算
,并证明
在
上单调递增;
(2)对任意的
,
,总存在
,使得
成立,求t的取值范围?
![](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/09f21febe8749e5e598124c2f6bb4025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75c137b664f5c1b3368a55c3e7adb1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5409f79d5899f4822deaf275df1739c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab409bb25958c2f01c73e26042c6f51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea944fa5b7030c92f0d06e7e15c1c135.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/006dd721f6e19ee105cf6e3a10b69c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a47fb2689296e12a46e6a9b65e74ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e805e0506d37973afc0664ae0a6af0.png)
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2024-01-25更新
|
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2卷引用:重庆市渝中区巴蜀中学校2023-2024学年高一上学期1月期末数学试题
名校
解题方法
10 . 已知实数
,且函数
,
,
,
,
,当
时,
的最小值记为
.
(1)若
,求函数
的单调递减区间;
(2)
,
,
,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a380067a20c25338eb0312e8df6c2760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7051b8cbec548d942b62fd290db4460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383330e8699c6ce53da6c5aaa70097d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/442a82cb501aeda22a086a2fe7ef7cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e9ac469995de3fcccf9300fbe8c68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edb160b3d56fdc5cb2123cbcac44c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f7dbb416ec1ff1984a724a4f48bf692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b3ae7e5228fd1acb0d46f6941143a7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe7341e9d43f8456a913620d9938205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6dd3fa42436802a270cd2ff46ba51d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be555d216bf07f824f3164f05e1cb72.png)
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2022-11-11更新
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3卷引用:重庆市南开中学校2022-2023学年高一上学期11月月考数学试题