名校
解题方法
1 . 用数学的眼光看世界就能发现很多数学之“美”.现代建筑讲究线条感,曲线之美让人称奇.衡量曲线弯曲程度的重要指标是曲率,曲线的曲率定义如下:若
是
的导函数,
是
的导函数,则曲线
在点
处的曲率
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/6acbc5be-bc56-4160-aee4-cfcd2cd3f43a.png?resizew=276)
若曲线
与
在
处的曲率分别为
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff61ecc0e66164caaf60511ea9500a4.png)
______ ;设正弦曲线
曲率为
,则
的最大值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13a9a154a651efb83f4b0cc4ae8f3cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fa72fc4959804b944bfaa93dbe2b21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35aeeb3025f23681786311c951a44a78.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/19/6acbc5be-bc56-4160-aee4-cfcd2cd3f43a.png?resizew=276)
若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d923750277c4ae4f8a7db57254c635b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294ed75f9d437ffc32235bcb602365c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832f2474efe89961ef41e884da7660c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f10dfc144c8970e4dde2f7bfcebd1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff61ecc0e66164caaf60511ea9500a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bbbe5ac4f60ab4004a43d16c0d4456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2581192317ef233ccdccfc48ac29b52b.png)
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