1 . 我国古代数学名著《九章算术》的论割圆术中有“割之弥细,所失弥少,割之又割,以至于不可割,则与圆周合体而无所失矣.”它体现了一种无限与有限的转化过程.比如在表达式
中“...”即代表无数次重复,但原式却是个定值,它可以通过方程
求得
.类比上述过程,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fdf504a4f533b0d3990832daae0b860.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e79197bce5d1859fcbfeadd6218f3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6977b6bb77c43822da13161ab1e674bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e3a9c7590825bfeeff83359c2513346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fdf504a4f533b0d3990832daae0b860.png)
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2 . 已知柯西不等式的向量形式为:设
是两个向量,则
,当且仅当
时,等号成立.若将
和
代入
,计算化简可得三维形式的柯西不等式:
,当且仅当
时,等号成立.若已知
,根据三维形式的柯西不等式可求得
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd6c0aa8a1d9413beeccecfc1a5ba1c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f27073df9ca7d76fb4b9e0d3d8e6f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa242a588b4880fc4d61815ae963a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1892e65161b5e5b0857c14004a80d8f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2287e7ac3ca75ee33913c8058da28e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f27073df9ca7d76fb4b9e0d3d8e6f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d482ac4f9f1c1bbff2709f3787fbcc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa242a588b4880fc4d61815ae963a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42d412d5a5c13e17ebc05ad19c098b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dd4067a19eeb07474557fe7b2508880.png)
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2021-12-12更新
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242次组卷
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2卷引用:云南省玉溪第一中学2021-2022学年高二上学期期中考试数学(理)试题