解题方法
1 . 若函数
的定义域、值域都是有限集合
,
,则定义
为集合A上的有限完整函数.已知
是定义在有限集合
上的有限完整函数.
(1)求
的最大值;
(2)当
时,均有
,求满足条件的
的个数;
(3)对于集合M上的有限完整函数
,定义“闭环函数”如下:
,对
,且
,
.若
,
,
,则称
为“m阶闭环函数”.证明:存在一个闭环函数
既是3阶闭环函数,也是4阶闭环函数(用列表法表示
的函数关系).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d677b98bf6b39322ba1be58a4def3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47eed557063f07462d7dbe78da5ec3e2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb29bacf2fcc07be37f89f9ad7a7faf.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6032aee742b136f8ea08073426fcb2d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d1ff786e39d2fce9e79a2ea3e969e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
(3)对于集合M上的有限完整函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e39e176af5b23719580d925e792aa8b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf5776ec7059c208daf01ca48a34915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c88248a34d270530f9d01570a911878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7149bd8132fd52cec51ae0f29986157a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c15f41c30653e445108fe7d3d8aa0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f29c06a3e9a73e905eb87d71efa201c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd09c401bb5423fb9272cad59a5e079a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
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名校
解题方法
2 . 定义函数
的曲率函数
(
是
的导函数),函数
在
处的曲率半径为该点处曲率
的倒数,曲率半径是函数图象在该点处曲率圆的半径,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d041d9b97b49fd58649bf68c0ff0acda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3bbfab935fafa320623f7e1438396.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4d2174f411d9db6ab7b2aea47818cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d8d167cd1eeed1b2b87267cd449051.png)
A.若曲线在各点处的曲率均不为0,则曲率越大,曲率圆越小 |
B.函数![]() ![]() |
C.若圆![]() ![]() ![]() |
D.若曲线![]() ![]() ![]() |
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解题方法
3 . 如图,在四棱锥
中,底面是边长为
的正方形,
为
的中点.
,过
作平面
的垂线,垂足为
,连
,
,设
,
的交点为
,在
中过
作直线
交
,
于
,
两点,
,
,过
作截面将此四棱锥分成上、下两部分,记上、下两部分的体积分别为
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13738f8488cb0750c8850ab2973bcf44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55bb0405afa96ebf94c5b03fd52763dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495ce311318aebbd108b2dc7cf317f45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/815d1ce1ba84bac399c8b20e074cf045.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149599d4161ac0e6ef91e06aef47029d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5bdbbd3084ddc946e12d530d2192522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8db072e2b6104671b82f948012fb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aeda46393004770ea79f8ba926029c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0a09d243c7fe7c0f8988582ac3da14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46bd37096f7014e00fd079823b6c3c3.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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|
782次组卷
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3卷引用:河南省漯河市高级中学2024届高三下学期3月检测数学试题(一)
名校
解题方法
4 . 在空间直角坐标系
中,三元二次方程所对应的曲面统称为二次曲面.比如方程
表示球面,就是一种常见的二次曲面.二次曲面在工业、农业、建筑等众多领域应用广泛.已知点
是二次曲面
上的任意一点,且
,
,
,则当
取得最小值时,不等式
恒成立,则实数
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338ac09ffd9addc3dadf363152c3e39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bfcaf2a345411411cf94422703e9269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3289a60a80d14f4b5399c31885280b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cad3aaeb5b444feb152378278f68863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a1be5c1350d02543a96399cc14a51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/381fb0e2caff5c1e03977ce2ecf46756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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|
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6卷引用:河南省濮阳市第一高级中学2021-2022学年高三上学期第一次质量检测理科数学试题
河南省濮阳市第一高级中学2021-2022学年高三上学期第一次质量检测理科数学试题湖北省鄂东南三校2022届高三下学期5月联考数学试题(已下线)专题08 导数及其应用(模拟练)(已下线)数学(上海A卷)上海市南模中学2024届高三上学期期中数学试题(已下线)第5章 导数及其应用(基础、常考、易错、压轴)分类专项训练(原卷版)
5 . 已知
,
,且
.给出如下结论(1)
;(2)
;(3)
;(4)
.其中正确结论是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0461e58768176f4e17ceaf5694be1ae5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57b29f52d5e2da5b86ef1d1e36655575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbb2fa016e9f01032952294c9827e222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2c4fd2d2d0027353b33b3903acc6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/717b691e0ded3a9bcd9228c04064a399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5e7fda3c5a53cc04b427fad6f1b9b1.png)
A.(1)(3) | B.(1)(4) | C.(2)(3) | D.(2)(4) |
您最近一年使用:0次
名校
6 . 在三棱锥
中,
平面ABC,
,
与
的外接圆圆心分别为
,
,若三棱锥
的外接球的表面积为
,设
,
,则
的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4f6f74444b2b7947fc6e35c8d62322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95345846d2dd4dfa042a9093c62a8b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b9520075fd378c3c736bb7a813281c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0445fae8dfe393af319b3da2811fbf53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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1697次组卷
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8卷引用:河南省顶级名校2022-2023学年高三上学期第一次月考试卷数学(理)试题
7 . 某地准备在山谷中建一座桥梁,桥梁及山谷的竖直截面图如图所示,谷底为点O,
为铅垂线(
在桥梁AB上).以O为原点建立直角坐标系,左侧山体曲线AO的方程为
,右侧山体曲线BO的方程为
,其中x,y的单位均为m.现在谷底两侧建造平行于
的桥墩CD和EF,其中C在线段
上,E在线段
上,且
m,
.
![](https://img.xkw.com/dksih/QBM/2021/12/25/2880222361378816/2886346853195776/STEM/339bfc80b4dd471c966f8a12f342d7f3.png?resizew=284)
(1)求CE的长;
(2)为了增加桥梁的结构强度,要在桥梁上的C,E之间找一点P,修建两个支撑斜柱DP和FP,当
最大时,求CP的长.(结果精确到0.1m,参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abbe2aba242716238b79c46bb1f40e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f327a9a8f969225929a4b9d2fc83576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a60ad7dfc9b8a902adbbf3bca3bdcdf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd37244e07a7f1e6b0d8afdb469cf76e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913d2a71d4012f2e38a2fc3a1d33d389.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c353ad1aadb0c8680d9901bf9dc43b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad34aa4ab53b0f85f6f02d07968eeeec.png)
![](https://img.xkw.com/dksih/QBM/2021/12/25/2880222361378816/2886346853195776/STEM/339bfc80b4dd471c966f8a12f342d7f3.png?resizew=284)
(1)求CE的长;
(2)为了增加桥梁的结构强度,要在桥梁上的C,E之间找一点P,修建两个支撑斜柱DP和FP,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35b2acb865af089b1c4f872c99106d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a8d188d7961d71439fdb53f9dbeaeb.png)
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3卷引用:河南省名校联盟(十所名校)2021-2022学年高三上学期12月考文科数学试题
名校
解题方法
8 . 已知点
,
分别为椭圆
的左、右焦点,点
在直线
上运动,若
的最大值为
,则椭圆
的离心率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6b94e42869013745050aba059b58dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f4f873802a24e7756eeab918c9a1c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22a3c7e465a61e9849dd223261be47c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
3392次组卷
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7卷引用:河南省部分名校2021-2022学年高三上学期8月份摸底联考数学(文)试题
河南省部分名校2021-2022学年高三上学期8月份摸底联考数学(文)试题河南省部分名校2021-2022学年高三上学期8月份摸底联考数学(理)试题河南省洛阳第一高级中学2021-2022学年高三上学期10月月考数学理科试题(已下线)第十一章 圆锥曲线专练3—椭圆的离心率1-2022届高三数学一轮复习(已下线)9.3 椭圆(精练)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)(已下线)专题16 椭圆(选择题、填空题)-备战2022年高考数学(文)母题题源解密(全国甲卷)(已下线)专题25 圆锥曲线压轴小题必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)
名校
解题方法
9 . 在
中,若
,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b339d390d7cf2d7750af0296d2e2afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e5d4f93699f8dcffb0e7840ca5597e.png)
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2020-06-03更新
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6卷引用:2020届河南省商丘周口市部分学校联考高三5月质量检测数学(文科)试题
2020届河南省商丘周口市部分学校联考高三5月质量检测数学(文科)试题河南省2020届高三5月份名校联盟高考数学(文科)模拟试题河南省名校联盟2020届高三5月质量检测数学文科试卷黑龙江省漠河市高级中学2020-2021学年高三上学期第一次摸底考试文科数学试题(已下线)考点24 正弦定理、余弦定理(考点专练)-备战2021年新高考数学一轮复习考点微专题黑龙江省哈尔滨市香坊区第六中学校2020-2021学年高三上学期期末数学试题
10 . 已知椭圆
的左、右焦点分别为
,
,上、下顶点分别为
,
,直线
的倾斜角为
,椭圆上的点到焦点的最大距离为3.
(1)求椭圆
的标准方程;
(2)若经过左焦点
的直线
与椭圆
交于
,
两点,且
,
两点均在
轴的左侧,记
和
的面积分别为
和
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014b99f5c93a4ce8cd6251c12c1d1b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
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