![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9c1e84aaa7e1b5c1283075b36c72fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcb55ae794081fa9e39ea5657fa5d41e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)奥古斯丁•路易斯・柯西,法国著名数学家.柯西在数学领域有非常高的造诣.很多数学的定理和公式都以他的名字来命名,如柯西不等式、柯西积分公式.其中柯西不等式在解决不等式证明的有关问题中有着广泛的应用.
①用向量证明二维柯西不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1befdda5f9e5055b0d2ae58b1b4b201.png)
②已知三维分式型柯西不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1358300202bcbca3c7a48fa40217a4ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5ba135022def1bcc1cddea66496706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f8e0e66571238a7e1c756b99b3113d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0e08a39c6619123557148d195abfbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927456b0989846a2f1573844bbaa2105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d731994627d9911585d053afc821e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6ce02259a85ea191541f4a708738f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98908c3834d8a95cadda737a9a1997bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b166cd7bc824fd798bbc544f837bd5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d98512b9538ceb0a008f74c0955f261f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
我们知道,我国早在《周髀算经》中就有“周三径一”的古率记载,《隋书•律历志》有如下记载:“南徐州从事史祖冲之更开密法,以圆径一亿为丈,圆周盈数三丈一尺四寸一分五厘九毫二秒七忽,肭数三丈一尺四寸一分五厘九毫二秒六忽,正数在盈肭二限之间.密率:圆径一百一十三,圆周三百五十五.约率,圆径七,周二十二”,这一记录指出了祖冲之关于圆周率的两大贡献:其一是求得圆周率
;其二是得到
的两个近似分数即:约率为22/7,密率为355/113,他算出的
的8位可靠数字,不但在当时是最精密的圆周率,而且保持世界纪录一千多年,他对
的研究真可谓“运筹于帷幄之中,决胜于千年之外”,祖冲之是我国古代最有影响的数学家之一,莫斯科大学走廊里有其塑像,1959年10月,原苏联通过“月球3”号卫星首次拍下月球背面照片后,就以祖冲之命名一个环形山,其月面坐标是:东经148度,北纬17度.
纵横古今,关于值的研究,经历了古代试验法时期、几何法时期、分析法时期、蒲丰或然性试验方法时期、计算机时期,已知
,试以上述
的不足近似值
和过剩近似值
为依据,那么使用两次“调日法”后可得
的近似分数为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0195f699765021e2c6ea985e487971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cae2e54eca2ffc297a015c561e30ac1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f239c63bc8bc3e5114063c76e8a975f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/580bddf0ec75a9918b9ddf18f9850cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e5f8881bd45e0a7ae54fe1ea0ff2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba361a7a2482a4e7ebe066fa29fc873.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26443543e190f15783a2309f7d44381e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b227d13609e34d3bd484db5de8c4be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ff4f7f57a89b6bce9d0a3c1976251d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b72d4b4a8f175d4d24cd8ef24a62c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)