1 . 给出集合
{
对任意
,都有
成立}.
(1)若
,求证:函数
;
(2)由于(1)中函数
既是周期函数又是偶函数,于是张同学猜想了两个结论:命题甲:集合M中的元素都是周期为6的函数:命题乙:集合M中的元素都是偶函数;请对两个命题给出判断,如果正确,请证明;如果不正确,请举反例:
(3)设p为常数,且
,求满足
成立的常数p的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9163ebe812708ee5337d62298c2e3363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc163d35aa285e48bcc21d6e392b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b005e1e4b8e41c0028cd464835c464.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2d58d309affa76c49e442468c013dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5314a9d2205a2beba0dcffb8fd943b18.png)
(2)由于(1)中函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2d58d309affa76c49e442468c013dd.png)
(3)设p为常数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c7f87b7ddd102e6a5e9cfb282bb47ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06a648a9da06fd9b05bb13cb8a5c047.png)
您最近一年使用:0次
名校
解题方法
2 . 设函数
定义在区间
上,若对任意的
、
、
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177e54e8deea5da9dc6bc82eb3de0c2c.png)
,当
,且
时,不等式
成立,就称函数
具有M性质.
(1)判断函数
,
是否具有M性质,并说明理由;
(2)已知函数
在区间
上恒正,且函数
,
具有M性质,求证:对任意的
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
,且
,有
;
(3)①已知函数
,
具有M性质,证明:对任意的
、
、![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
,有
,其中等号当且仅当
时成立;
②已知函数
,
具有M性质,若
、
、
为三角形
的内角,求
的最大值.
(可参考:对于任意给定实数
、
,有
,且等号当且仅当
时成立.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9c587f6257331045c362ef25677c20.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/770cf3716f1e9dc8023a898df7f33783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177e54e8deea5da9dc6bc82eb3de0c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d589f18d16b1a6bbd5108409c53fd05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a49c641617f38855f6abc7baf36af8e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f05279fb93940ea0741b64227cc58c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a70644524df044d4a24b998a81d44c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6881a170f6ef9ed5c133b95c2f448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475a20b276768b190ac15c9aa5c352ef.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9c587f6257331045c362ef25677c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80fcd5a1ca4f9abf76c88db3a3542b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5348b540c0b2e012191ae95351aaac.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/9d589f18d16b1a6bbd5108409c53fd05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450fb41cf5543a06035606ff29a9e934.png)
(3)①已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5348b540c0b2e012191ae95351aaac.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d589f18d16b1a6bbd5108409c53fd05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f183be2a65b185fd240990dffdec3ba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62e63003be4ad8c4c51e36e71df2ac3.png)
②已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089e6e44271b4c08be46dda1e7403741.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/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a8080fef9bdfa92ae70f3e314eef3e3.png)
(可参考:对于任意给定实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/205ca5a7d5bede14db0175445bb6d508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6b79d363c080275b93b8cc4b279653.png)
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2021-12-27更新
|
699次组卷
|
5卷引用:上海市黄浦区2022届高三一模数学试题
上海市黄浦区2022届高三一模数学试题(已下线)上海市黄浦区2022届高三上学期一模数学试题上海市文来高中2023届高三上学期期中数学试题(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)(已下线)第04讲 函数最值与性质-3
名校
解题方法
3 . 在数学中,双曲函数是与三角函数类似的函数,最基本的双曲函数是双曲正弦函数与双曲余弦函数,其中双曲正弦函数:
,双曲余弦函数:
.(e是自然对数的底数,
).
(1)计算
的值;
(2)类比两角和的余弦公式,写出两角和的双曲余弦公式:
______,并加以证明;
(3)若对任意
,关于
的方程
有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3321510a9eb73909a36c084a8630e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0099b9b80ed478824fa95677ebe9d5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e694af0c9f990ecb8b54b1c08bcc578e.png)
(2)类比两角和的余弦公式,写出两角和的双曲余弦公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92c32edc0e000405b7a6b9c48549959.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f78f05631a2ecb8bc3d379ca6c81f93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed807cc52eca7b462a3850b5e5e02b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-06-21更新
|
991次组卷
|
7卷引用:上海市宝山区2022-2023学年高一下学期期末数学试题
上海市宝山区2022-2023学年高一下学期期末数学试题上海市闵行(文琦)中学2023-2024学年高一下学期3月月考数学试卷(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)(已下线)模块六 专题5 全真拔高模拟1(已下线)专题14 三角函数的图象与性质压轴题-【常考压轴题】山东省济南市山东师大附中2022-2023学年高一下学期数学竞赛选拔(初赛)试题(已下线)第10章 三角恒等变换单元综合能力测试卷-【帮课堂】(苏教版2019必修第二册)
解题方法
4 . 对于一个向量组
,令
,如果存在
,使得
,那么称
是该向量组的“好向量”
(1)若
是向量组
的“好向量”,且
,求实数
的取值范围;
(2)已知
,
,
均是向量组
的“好向量”,试探究
的等量关系并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153cbba188fca9ff2e6b31a49d5b6229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31866ce53f59ecf68618ac87f37d721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0d561daae579f69538ace2a8f00916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9d5830f763967adbf6db9c5d1cc4af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf315b7361dbc0af56a1c515d32216c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb6823d280520da116cf1bc3943cf42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4110b20b2c0f07c2688bf3a48d7ff68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c0f3eb9b0030afe2ed4799a984ce7cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a223991a4ec2ca30469960f093ddb1c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc72f5677dda2b1de520c4cc3c1ceb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb6823d280520da116cf1bc3943cf42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4110b20b2c0f07c2688bf3a48d7ff68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4110b20b2c0f07c2688bf3a48d7ff68.png)
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2021高一下·上海·专题练习
名校
5 . 对于集合
和常数
,定义:
为集合
相对
的“余弦方差”.
(1)若集合
,
,求集合
相对
的“余弦方差”;
(2)若集合
,证明集合
相对于任何常数
的“余弦方差”是一个常数,并求这个常数;
(3)若集合
,
,
,相对于任何常数
的“余弦方差”是一个常数,求
,
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f54ae4188477aadfe6b7aaacab5f55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a04b47c230bef1c678a384275af5cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
(1)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5063cae47b07f9d87a072c0122dd1fee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35272ddbd63d2485769020d9839445f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbed16abdf2be6944bebed87c822254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c0118c18819bc01cb18084f808cc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7cbba6f130b84315180391c177d0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90017bd261a3784dc0dab3c3e6c0ff1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4438bae1705c0f26beddf41322c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
您最近一年使用:0次
2022-04-30更新
|
483次组卷
|
8卷引用:第6章 三角(章节压轴题解题思路分析)-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6章 三角(章节压轴题解题思路分析)-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)上海市奉贤中学2021-2022学年高一下学期3月月考数学试题上海市金山中学2021-2022学年高一下学期3月月考数学试题(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)北京八中2021-2022学年高一下学期期中数学试题(已下线)10.3 几个三角恒等式(分层练习)-2022-2023学年高一数学同步精品课堂(苏教版2019必修第二册)北京市第八中学2021-2022学年高一下学期期中考试数学试题北京市门头沟区大峪中学2023-2024学年高一下学期期中数学试卷
名校
解题方法
6 . 已知向量
与向量
的对应关系用
表示.
(1)证明:对任意向量
、
及常数
、
,恒有
;
(2)设
,
,求向量
及
的坐标;
(3)求使
(
、
为常数)的向量
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b91b0e5ad368c6da34f2263de056fee5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794953fe619ca196431d6beaa0076e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa48cf7be8957cd677297267735bee62.png)
(1)证明:对任意向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f2c07ad0724802023f1e232aed55ff1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479779070b95c1c2845f0a24dc8d5f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4568d49578f17e744a5d6f6b5d2ed4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17f98350f6070505458786e9953eb99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5917359f912d80b0a4ba3269aa91e6dd.png)
(3)求使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac6d4148ee2d5baa49302c6049eded0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
您最近一年使用:0次
名校
7 . 在平面上,给定非零向量
,对任意向量
,定义
.
(1)若
=(-1,3),
=(2,3),求
;
(2)若
=(2,1),位置向量
的终点在直线x+y+1=0上,求位置向量
终点轨迹方程;
(3)对任意两个向量
,求证∶
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9181079d14f7c1bc9b5b2624f94edca.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f2d19b69f787a07ba6b8abe06802c0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f2d19b69f787a07ba6b8abe06802c0.png)
(3)对任意两个向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1721476f7850842ba3dc3d8be33c3723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835ebae7895448fd3d6551b953565ab3.png)
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名校
8 . 在直角坐标平面
上的一列点
,简记为
.若由
构成的数列
满足
,其中
为方向与
轴正方向相同的单位向量,则称
为
点列.
(1)判断
,是否为
点列,并说明理由;
(2)若
为
点列,且点
在点
的右上方.任取其中连续三点
,判断
的形状(锐角三角形、直角三角形、钝角三角形),并予以证明;
(3)若
为
点列,正整数
,满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c13b920ec4a33103954c68daa7644ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7836415e9b77334eee27c0d497ca5ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b7daef66f5d193befe316e6a9df2bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821a7c2e810ef18a2ee78f3722f03c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b7813755384e0b6044fe296d7c6029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a09e3d201f7699e8d480c768e34696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6edc135bb869e8e8dd68b711d147e368.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06dfbe171fd6d47d6b8ab101b62ac0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ada35c9021498f44a4c7cb9efd058bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e71cb7bfc09205b70196aeadad57439.png)
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2020-06-26更新
|
578次组卷
|
7卷引用:上海市奉贤中学2018-2019学年高二上学期10月月考数学试题
名校
解题方法
9 . 对于一个向量组
,令
,如果存在
,使得
,那么称
是该向量组的“长向量”
(1)若
是向量组
的“长向量”,且
,求实数
的取值范围;
(2)已知
,
,
均是向量组
的“长向量”,试探究
,
,
的等量关系并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d9c4e13c48813cb746b75ac8b842886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a589d1b2b9d250c545d81abd0282699a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2dac5a1e64f5297958618920ffcd70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752ed927125e4a75ae7c007db9c59683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71760f71b439f7d3cba6429f1bc4cfa.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde8b12aa232eeccc1e7ad1cc6d417c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a881c7a0b386a6fd3f43453a66197c28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07fbcd094482826c8759e06d899c7d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d970a4c8abf3fe4da3382206086a6cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2bc63bd663aed17c3b584ec105b7b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde8b12aa232eeccc1e7ad1cc6d417c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a881c7a0b386a6fd3f43453a66197c28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d970a4c8abf3fe4da3382206086a6cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2bc63bd663aed17c3b584ec105b7b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cde8b12aa232eeccc1e7ad1cc6d417c1.png)
您最近一年使用:0次
10 . 已知函数
,若存在实数
,使得对于定义域内的任意实数
,均有
成立,则称函数
为“可平衡”函数,有序数对
称为函数
的“平衡”数对.
(1)若
,判断
是否为“可平衡”函数,并说明理由;
(2)若
,
,当
变化时,求证:
与
的“平衡”数对相同;
(3)若
,且
、
均为函数
的“平衡”数对.当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4576aca200298ff65cae7e122932ff86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e76b43fa87a022251c67fd1aba814f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa6e6840235cbfe76f9827fc755d4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7f9b35017daa8b524c5717a355834a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a0d83b10930e2a4287b3676927e455.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e1bb4d16cb313c57c2e7d3a2917fc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6041d40b75e7bb0e8d34c34c2c0b975a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ef993cbb9207da9972cfbf0eadea0b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2448d324024e6277c4ce46d6ab90fe0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1409480b5d8e342a38b918039a31b806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ce92f59ccf725aeed263923f2e7082.png)
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