二维空间中圆的一维测度(周长)
,二维测度(面积)
,观察发现
;三维空间中球的二维测度(表面积)
,三维测度(体积)
,观察发现
.已知四维空间中“超球”的三维测度
,猜想其四维测度![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b4db8437c6d4376b55bdceed535b0bb.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8469d348cd31a3a1429e0828954d6164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50390afd2cf9ed105ad1f9e1873d7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b5401112e436df464ae3fcaa3ebf447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68159e318b99528a6e641f9b8804ec8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab8dd1a91f4087c0386c9d1d50a22c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08322652b0e4ad5c32988a1a85bc7a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a545e92f552f30a155b4c53c71747d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b4db8437c6d4376b55bdceed535b0bb.png)
更新时间:2016-01-21 06:35:10
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解题方法
【推荐1】已知曲线
在点
处的切线斜率为
,则当
时的
点坐标为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c904567c3b3734e1eca8d042ef7a7b2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367e788c32187ae2cc97aaa24da1d40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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【推荐2】已知过原点的直线与曲线
相切,则该直线的方程是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
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名校
【推荐1】在复平面内,若向量
对应的复数是1,将向量
绕O点逆时针旋转
得到向量
,则向量
对应的复数是
.由类比推理得:若向量
对应的复数是
,将向量
绕O点逆时针旋转
得到向量
,则向量
对应的复数是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b0ab2519d0fb666743993961daee47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b0ab2519d0fb666743993961daee47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61329657aa12a3b1b4f9bb09cb7f6860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828c23f68b6fc90f705a9d691bcfab35.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
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【推荐2】定义一种新运算“*”,对自然数
满足以下等式:(1)1*1=1;(2)
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c7ef71bfb4e9c24baf866f9f099c38.png)
_________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56bc3de174b8c78889f209943addcc5c.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a232d47ae706649d2b9604f1ade3eca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c7ef71bfb4e9c24baf866f9f099c38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56bc3de174b8c78889f209943addcc5c.png)
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【推荐3】黄金比例,用希腊字母Φ表示,借用古希腊数学家欧几里德的话:当整条线段的长度与线段中较长段的比例等于较长段与较短段的比例时,就是根据黄金比例来分割线段.用A,B分别表示较长段与较短段的线段长度,于是将欧几里德的描述用代数方法表示出来:Φ=
,从可以解出Φ的值.类似地,可以定义其他金属比例.假设把线段分成n+1段,其中有n段长度相等,记这n段的每一段长为A.面剩下的一段长为B (长度较短的).如果A与B之比等于整条线段的长与A之比,我们用
来表示这个比例,即
=
对于n(n
)的每个值对应一个
,则称
为金属比例.当n=1时,即为黄金比例,此时Φ=
;当n=2时,即为白银比例,我们用希腊字母
表示该比例,则
____
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca3b21432a1340b673a37d48a1a42b3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17073d8969075d4513a9b03b0f5ca71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17073d8969075d4513a9b03b0f5ca71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a601b9060badde0d5dcb68d14709d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fb095ca269bf16da403dbf39929326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17073d8969075d4513a9b03b0f5ca71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f17073d8969075d4513a9b03b0f5ca71.png)
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