名校
解题方法
1 . 已知
,若存在
,使得
,则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6604efa9b381b2c8488cbf595161fc8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4b767e45047cd9f5d0845c700a5359.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba640401216f7fea2c82c230d847d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
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2024-06-13更新
|
153次组卷
|
2卷引用:江苏省无锡市江阴长泾中学2023-2024学年高二下学期5月阶段检测数学试卷
2 . 对于三次函数
,给出定义:设
是函数
的导数,
是函数
的导数,若方程
有实数解
,则称点
为函数
的“拐点”.某同学经过探究发现:任何一个三次函数都有“拐点”;任何一个三次函数都有对称中心,且“拐点”就是对称中心.给定函数
,请你根据上面的探究结果,解答以下问题:
①函数
的对称中心坐标为______ ;
②计算![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634577ca265c60d146b9d28661e24c4b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75044e0301ef9def5c1a1c8e6f2cba77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac282e92da3691942a6ba8511de2303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc581690f1d82133bb5fed3d7f365f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db46d62d4c778babb46a0a3d223384e5.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db46d62d4c778babb46a0a3d223384e5.png)
②计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634577ca265c60d146b9d28661e24c4b.png)
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2024-05-06更新
|
337次组卷
|
2卷引用:江苏省无锡市锡东高级中学2023-2024学年高二下学期期中考试数学试题
名校
3 . 如今中国在基建方面世界领先,可谓是逢山开路,遇水架桥.公路里程、高铁里程双双都是世界第一.建设过程中研制出用于基建的大型龙门吊、平衡盾构机等国之重器更是世界领先.如图是某重器上一零件结构模型,中间最大球为正四面体
的内切球,中等球与最大球和正四面体三个面均相切,最小球与中等球和正四面体三个面均相切,已知正四面体
体积为
,则模型中最大球的体积为________ ,模型中九个球的表面积之和为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6093eebca8f3ff82ce9298feb197e955.png)
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2024·全国·模拟预测
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4 . 已知函数
的图象关于点
对称,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023768759ff95c1fc51b3231a87fa098.png)
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3942b3ffb224601a33dd6fecd10a61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da39bc5be89d23c682ba9578a4abba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/023768759ff95c1fc51b3231a87fa098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b65db4e6769b2e40b9f43b7864f145f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1283d27a76d6f89b9f6201691c30cfcd.png)
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名校
解题方法
5 . 已知向量
,
夹角为
,
,若对任意
,恒有
,则函数
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fa8ea29001bb1f0c1e5157aff2fca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d967e63a1bf0e3c07a26b09c4ff008a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1984a476bd436c4f8fdc434092e59091.png)
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2024-04-03更新
|
864次组卷
|
2卷引用:江苏省无锡市第一中学2023-2024学年高一下学期阶段性质量检测(3月月考)数学试题
名校
解题方法
6 . 已知四边形
中,
,
,设
与
面积分别为
,
.则
的最大值为__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce519312a849963b376c202c3f9d7cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93fb5a916bc3f6945a490356aa3b5582.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be89b91f05f281190209b1e876299d57.png)
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名校
7 . 已知函数
有两个极值点
,则
的取值范围为________ ;若函数
有两个极值点
,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598b0aa4c26c55d72bd854fce89ac1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae869654e1480c01214922f07644380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00871ac2e64006d5f7d0950dc6b25a12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30abc4ebbc94f3cd022c06bf432bdfb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d46ba782625c277edcf835446700c4aa.png)
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2024-03-28更新
|
395次组卷
|
3卷引用:江苏省无锡市江阴市四校2023-2024学年高二下学期期中联考数学试题
名校
8 . 已知函数
,过点
且与曲线
相切的直线只有1条,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c30d01fc06211afbdb725d37d456f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c17110dba6a1ddf771e188afa8218a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2024-03-27更新
|
418次组卷
|
2卷引用:江苏省无锡市市北高级中学2023-2024学年高二下学期期中检测数学试题
名校
解题方法
9 . 若实数x,y满足
,则
的最大值为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a143573e9fe53e6a861154bf5b4c27c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3345715f6a5c7f80a4898d1745b01bb.png)
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2024-03-20更新
|
1621次组卷
|
5卷引用:江苏省无锡市锡东高级中学2024届高三下学期4月月考数学试题
江苏省无锡市锡东高级中学2024届高三下学期4月月考数学试题安徽省芜湖市安徽师范大学附属中学2024届高三第二次模拟考试数学试题安徽省天域全国名校协作体2024届高三下学期联考(二模)数学试题(已下线)安徽省天域全国名校协作体2024届高三下学期联考(二模)数学试题变式题11-15(已下线)压轴题06向量、复数压轴题16题型汇总-1
解题方法
10 . “曼哈顿距离”是人脸识别中的一种重要测距方式,其定义如下:设
,
,则
,
两点间的曼哈顿距离
已知
,点
在圆
上运动,若点
满足
,则
的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c04bbc507d8f917da5253fca7f2c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a5862f87bdbd8d6c653905cddb9900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f6ae1c2a81078eac5ed2f4f823b671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b83e2fc66e8ab0e6f60a1790cea6c1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de86d9c0675d246a280f6b71a68aaf9d.png)
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