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1 . 点
为
平面上一点,有如下三个结论:
①若
,则点
为
的______;
②若
,则点
为
的______;
③若
,则点
为
的______.
回答以下两个小问:
(1)请你从以下四个选项中分别选出一项,填在相应的横线上.
A. 重心 B. 外心 C. 内心 D. 垂心
(2)请你证明结论②.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6740b373e829124a9f0728a644e829ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5965f05ab9d3d721515717affeaa4d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a074d407b957f752244c9b5a06dc488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
回答以下两个小问:
(1)请你从以下四个选项中分别选出一项,填在相应的横线上.
A. 重心 B. 外心 C. 内心 D. 垂心
(2)请你证明结论②.
您最近一年使用:0次
18-19高一下·上海浦东新·期末
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2 . (1)证明:
;
(2)证明:对任何正整数n,存在多项式函数
,使得
对所有实数x均成立,其中
均为整数,当n为奇数时,
,当n为偶数时,
;
(3)利用(2)的结论判断
是否为有理数?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d969abdb2f6638663e80e15bffd247.png)
(2)证明:对任何正整数n,存在多项式函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2b21d31f1bb8801b0117b49086a634.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a68a728745bb3bd33917dc715c4fc945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bd42f8e3f220a7b1c6f6945e73bc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feaffe7219b4b165cf67c7751dff8876.png)
(3)利用(2)的结论判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d82121ba82f39bb5e8068bd11ed6d74.png)
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3 . 奔驰定理:已知
是
内的一点,
,
,
的面积分别为
,
,
,则
.“奔驰定理”是平面向量中一个非常优美的结论,因为这个定理对应的图形与“奔驰”轿车(Mercedes benz)的logo很相似,故形象地称其为“奔驰定理”若
是锐角
内的一点,
,
,
是
的三个内角,且点
满足
,则必有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4962343ca7d065aee473dbf79eb8d3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3304bc1372275307dce0bf4e98b8f3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2981bf2261343f905ec1b5355a3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319b6a5373bc8eb13772b8e6d047779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea3c7cd2f23b4521e64a7e64844ec48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089e8a7f6c535fc3cd270af428d55f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9659621d48404d8e5479cbab9050e5a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec09a159d6760fca8ae5966bf97b4e49.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2019-12-04更新
|
2839次组卷
|
5卷引用:河南省南阳市2019-2020学年高三上学期期中数学(理)试题
河南省南阳市2019-2020学年高三上学期期中数学(理)试题湖南省邵阳市武冈市2021-2022学年高一下学期期中数学试题(已下线)平面向量专题:奔驰定理解三角形面积比值问题-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)(已下线)第五篇 向量与几何 专题13 奔驰定理 微点2 奔驰定理(二)(已下线)专题突破卷15 三角形的“四心”及奔驰定理
4 . 已知
的外接圆圆心为O,
,
,若
(
为实数)有最小值,则参数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eb0faeb1a3c901d6dde395ea54c4b24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec82cb48f645fc7f42c2f69f348e183a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe5eb123e1fb5972c0f784f303c70c8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2019-11-19更新
|
3090次组卷
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12卷引用:湖北省武汉市东西湖区华中师范大学第一附属中学2019-2020学年高三上学期期中数学(理)试题
湖北省武汉市东西湖区华中师范大学第一附属中学2019-2020学年高三上学期期中数学(理)试题(已下线)3.1平面向量的概念及其性质[文] -《备战2020年高考精选考点专项突破题集》(已下线)3.1平面向量的概念及其性质[理]-《备战2020年高考精选考点专项突破题集》2020届安徽省淮北市濉溪县高三上学期第二次教学质量检测数学(理)试题2020届湖南省长沙市长郡中学高三月考(六)数学(理)试题山西省长治市第二中学校2019-2020学年高一下学期摸底数学(理)试题河北省衡水市枣强中学2020届高三下学期2月调研数学(理)试题(已下线)上海市浦东新区华东师范大学第二附属中学2021届高三4月高考数学模拟试题(已下线)上海市华东师范大学第二附属中学2021届高三下学期4月月考数学试题上海市上海中学2022-2023学年高一下学期期末数学试题湖北省温德克英联盟2023-2024学年高二8月开学综合性难度选拔考试数学试题(已下线)上海市高一下学期期末真题必刷03-期末考点大串讲(沪教版2020必修二)
名校
5 . 已知函数
,若存在
,
,…,
满足
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ac962cba47b78e51708df4540aa1ec.png)
,
,则
的最小值______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a098849c36301841964b456bde78df7.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/dad7f66c97bfce4c00c53d86700c961b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e050ee2552fd2334481ba5120318798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ac962cba47b78e51708df4540aa1ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34f6a0ae8ffead0853270e7cebaa8f7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2072474ae3470d313ffe9f553b4fcf4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
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6 . 定义在
上的函数
,若已知其在
内只取到一个最大值和一个最小值,且当
时函数取得最大值为
;当
,函数取得最小值为
.
(1)求出此函数的解析式;
(2)是否存在实数
,满足不等式
?若存在,求出
的范围(或值),若不存在,请说明理由;
(3)若将函数
的图像保持横坐标不变纵坐标变为原来的
得到函数
,再将函数
的图像向左平移
个单位得到函数
,已知函数
的最大值为
,求满足条件的
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e95c7a4e3c8035ca05485a5645c0811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb17ae5288f12565bb8be5c5cfccfff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ff420ca0d6e2e7d434a933cf6c5792b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2390fea4007021aa940827835aa9ad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81fb134b2b48acc99213fff6ccfee65f.png)
(1)求出此函数的解析式;
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e98270ff8bfa25a9ff3d4c51157cde4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eda96c08c50e3495200bb200175732e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/890527daa24d6782f6da453fb40fe03d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe84f65c9c4345ae5ddcdafa89e7273.png)
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2019-10-29更新
|
1880次组卷
|
2卷引用:江苏省苏州市震泽中学2019-2020学年高一(大杨班)上学期第一次月考数学试题
7 . 如图,在正方形
中,
为
的中点,
是以
为圆心,
为半径的圆弧上的任意一点,设
,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c2b8cc1fd7caa03f1308e9c9db6375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c032ffaa8007a88f7b637bc2b39df8cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/393cc436-f9c2-45eb-a14f-b0f7d09bf019.png?resizew=131)
您最近一年使用:0次
名校
8 . 已知函数
,
、
、
,且
都有
,满足
的实数
有且只有
个,给出下述四个结论:
①满足题目条件的实数
有且只有
个;②满足题目条件的实数
有且只有
个;
③
在
上单调递增;④
的取值范围是
.
其中所有正确结论的编号是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8066f6c7b05b1dc18c92c74b0d136688.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/da339231eefd022a41948b0971264d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/610cd64aad55489c32309b15b04b1b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c4020b17f7ad2d5f179b3f6b01898e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba35bd709f9499f46518bcdfa3a73e97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
①满足题目条件的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091358a4f8555a637e76c59b13dbe1ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f521eaa1bf88c61dffdfa9bc4a4f067c.png)
其中所有正确结论的编号是
A.①④ | B.②③ | C.①②③ | D.①③④ |
您最近一年使用:0次
2019-10-23更新
|
4460次组卷
|
6卷引用:四川天府名校2019-2020学年高三上学期教学第一轮联合质量测评理科数学试题
名校
9 . 如图,在
中,点
是线段
及
、
的延长线所围成的阴影区域内(含边界)的任意一点,且
,则在直角坐标平面上,实数对
所表示的区域在直线
的右下侧部分的面积是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/17/a4be3ec7-5a09-48b3-b433-380c690dc5eb.png?resizew=223)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8189f7b0ffe4d20bf0fad43b4ed589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d093706141016f4e2fde905738cd481e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72550f4d19fddb5488b394315f752966.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/17/a4be3ec7-5a09-48b3-b433-380c690dc5eb.png?resizew=223)
A.![]() | B.![]() | C.![]() | D.不能求 |
您最近一年使用:0次
2019-10-11更新
|
2705次组卷
|
5卷引用:人教A版 全能练习 必修4 第二章 滚动习题(三)
人教A版 全能练习 必修4 第二章 滚动习题(三)安徽省安庆市第一中学2018-2019学年高一上学期期末数学试题(已下线)专题7-1 线性规划归类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)(已下线)专题5-2 向量线性运算及四心综合归类 - 3(已下线)专题4 向量综合归类(讲+练)-1
10 . 已知抛物线
的焦点为
,过
作直线
交抛物线于
、
两点,且
(
为非零常数).以
为切点作抛物线
的切线交直线
于
点,则
的长度为________ .(结果用含
式子表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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