解题方法
1 . 曲线的曲率是描述几何弯曲程度的量,曲率越大,曲线的弯曲程度越大.曲线在点M处的曲率
(其中
表示函数
在点M处的导数,
表示导函数
在点M处的导数).在曲线
上点M处的法线(过该点且垂直于该点处的切线的直线为曲线在此处的法线)指向曲线凹的一侧上取一点D,使得
,则称以D为圆心,以
为半径的圆为曲线在M处的曲率圆,因为此曲率圆与曲线弧度密切程度非常好,且再没有圆能介于此圆与曲线之间而与曲线相切,所以又称此圆为曲线在此处的密切圆.
在点
处的曲率,并在曲线
的图象上找一个点E,使曲线
在点E处的曲率与曲线
在点
处的曲率相同;
(2)若要在曲线
上支凹侧放置圆
使其能在
处与曲线
相切且半径最大,求圆
的方程;
(3)在(2)的条件下,在圆
上任取一点P,曲线
上任取关于原点对称的两点A,B,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1992f681163b2b8d1fe2df9280225f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4d2174f411d9db6ab7b2aea47818cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc2b6c6aec8cfad1ce0277d6db9759c3.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/67466ba0dcffc70b783b0e1030f4d049.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171102a883b22fe6ca578efc8926f5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb734664b496f232b86d053650bb85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc58793b423b62b234768d0cb8be55e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/309092c6a1d81679c24dc598af8d6567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc58793b423b62b234768d0cb8be55e4.png)
(2)若要在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cbb734664b496f232b86d053650bb85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc58793b423b62b234768d0cb8be55e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
(3)在(2)的条件下,在圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
您最近一年使用:0次
2024-05-14更新
|
411次组卷
|
2卷引用:广东省茂名市高2024届高三下学期高考模拟数学试题
2 . 已知函数
,将满足
的所有正数
从小到大排成数列
.
(1)求
的通项公式.
(2)令
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb8827d041bc44dd083942aa7002222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbadbb09da422f97c3757082869fa50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4534863548123ea01546c6dd6029769.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
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3 . 已知抛物线
与直线
相交,求它们交点处的切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df4ab5ed446cb4d85ee8f9e93e0985e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae342dcb93e0e6f017093cacc5ac977.png)
您最近一年使用:0次
4 . 求曲线
过点
的切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c184c17e35b98fe8094cebe9522e1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa71aa2ea224669698850108751a71a.png)
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名校
5 . 已知函数
,其中
.
(1)当
时,求
的值;
(2)讨论
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/153b79d3d263ae875016cf001f5a93c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad3f9fa27837ba30d35304933dfb776.png)
(2)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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2022-02-25更新
|
2154次组卷
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6卷引用:广东省高州市2022届高三第二次模拟数学试题
6 . 已知函数的
图像在点
处的切线方程为
.
(1)求
的值
(2)求函数
在
值域.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ede0307fe68131cf9152da4f134ca8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c930fe3d329c6f1df78e266f2a30f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2c86b7d73e483ddba7269e60bc76ac.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f7de53cd13580b60572dd233c7ba976.png)
您最近一年使用:0次
2017-11-04更新
|
410次组卷
|
4卷引用:广东省茂名市五大联盟学校2018届高三9月份联考试理数试题