名校
1 . 设
为坐标原点,定义非零向量
,
的“相伴函数”为
,
向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57fd00cda9052ff2c07b3ff54751a9a7.png)
,
称为函数
的“相伴向量”.记平面内所有向量的“相伴函数”构成的集合为
.
(1)设函数
,求证:
;
(2)记
,
的“相伴函数”为
,若函数
,
,
与直线
有且仅有四个不同的交点,求实数
的取值范围;
(3)已知点
,
满足
,向量
的“相伴函数”
在
处取得最大值.当点
运动时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729e5e49fe4802e93526d94d47a8e35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b8cd2e8a9ae69fc0020962e444a2abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a69a16cf2aae32a6a8f814e7fbb3a64.png)
向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57fd00cda9052ff2c07b3ff54751a9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66c6ecdf8ced933e8e6657196acc924f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b8cd2e8a9ae69fc0020962e444a2abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65c6f29b2b1955715616003d51d8b77f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f72579537688c3fce17bdc500c67a1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4967b02dcf5b76c0d5ce82417618aad7.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94862c1d4c0cb6f8d88c79aec5fea94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad217e26bd3580c35998109de14cef73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f315885d6ef5e90995c5a2a52aebcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3038d4728f959a8efedc2592e4a4b5fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f486b99a92504148663e4d0fe94d73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead6a3dbd03539ef5e0807be57bb1e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20ad2e9e3a61b4dac3f48df7df62d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b8cd2e8a9ae69fc0020962e444a2abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91c44df6dc6d714b4f4f041a7d8a1ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00da1c29aea46e36cda0f5780966bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e0e24323fe73e5d9fc6136219306da.png)
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2019-12-28更新
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621次组卷
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2卷引用:江苏省南通市启东中学2019-2020学年高一上学期第一次质量检测数学试题(创新班)