名校
解题方法
1 . 如图所示,在底半径为
、高为
(
为定值,且
)的圆锥内部内接一个底半径为
、高为
的圆柱,甲、乙两位同学采用两种不同的方法来解决. 甲采用圆柱底面与圆锥底面重合的“竖放”方式(图甲),乙采用圆柱母线与圆锥底面直径重合的“横放”方式(图乙).
、
分别“竖放”、“横放”时内接圆柱的体积,用内接圆柱的底半径
为自变量分别表示
、
;
(2)试分别求
、
的最大值
、
,并比较
、
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359bf5e1f96347d26da78846710cd1e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ddca975d9281f5a23faa288882727b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
(2)试分别求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6e0de4744a73a855b8f10e319b1648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d442b6256850f32ffd233fd10e81fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a6e0de4744a73a855b8f10e319b1648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d442b6256850f32ffd233fd10e81fd0.png)
您最近一年使用:0次
2021-11-27更新
|
680次组卷
|
4卷引用:福建省福州第一中学2022届高三上学期期中考试数学试题
福建省福州第一中学2022届高三上学期期中考试数学试题(已下线)热点08 立体几何-2022年高考数学【热点·重点·难点】专练(新高考专用)(已下线)热点05 空间几何体表面积与体积的计算-2022年高考数学【热点·重点·难点】专练(全国通用)沪教版(2020) 选修第二册 经典学案 课后作业 第5章 5.3 导数的应用
解题方法
2 . 1.福建省平潭综合实验区澳前68小镇的猴研岛,是祖国大陆距宝岛台湾最近的地方,直线距离仅68海里.为了更好地完善硬件设施提升小镇旅游面貌,68小镇管理处在水泥路边安装路灯,路灯的设计如图所示,
为地面,
、
为路灯灯杆,
,
,在
处安装路灯,路灯采用可旋转灯口方向的锥形灯罩,灯罩的照明张角
,已知
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01dcbd171693a47c5b932a5e84de10c6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e382244f-f498-4708-a8e4-0310965a54f4.png?resizew=367)
(1)若
,求此路灯在路面OM上的照明宽度
;
(2)为了控制的路灯照明效果,令
,求此路灯在路面OM上的照明宽度
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338ab8f69b7c7ae39d3f242a59831573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15772c16f464359cd36394ddabaed15d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d1941f768aa9ab5ae0c7cdf6aab4ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf1967597e36c07196c680a6d42a9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01dcbd171693a47c5b932a5e84de10c6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/e382244f-f498-4708-a8e4-0310965a54f4.png?resizew=367)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d57678b93f1dcb18d4cbb33ff70bce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(2)为了控制的路灯照明效果,令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920fb585232679dfac915b1219033af5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
名校
解题方法
3 . 椭圆E:
,长轴长为4c(c为半焦距),左顶点为A,过点A作直线
与椭圆E交于另一个点P(点P在第一象限),P、Q两点均在椭圆上且关于x轴对称,点O为坐标原点,直线OP的斜率为
,直线
与△APQ的外接圆C(C为圆心)相切于P点,与椭圆交于另一个点T,且
;
![](https://img.xkw.com/dksih/QBM/2021/11/9/2847667282886656/2847861935218688/STEM/5f3f4a1f-aeb1-4e30-9c87-8061864b03fa.png?resizew=314)
(1)求椭圆E的离心率;
(2)求直线
与直线
的斜率;
(3)求椭圆E的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af2fdf1944afebb51cb6a5e6c74aadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eab7aa86b3345bf4703ffd7a521b390.png)
![](https://img.xkw.com/dksih/QBM/2021/11/9/2847667282886656/2847861935218688/STEM/5f3f4a1f-aeb1-4e30-9c87-8061864b03fa.png?resizew=314)
(1)求椭圆E的离心率;
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(3)求椭圆E的标准方程.
您最近一年使用:0次
2021-11-10更新
|
562次组卷
|
4卷引用:天津市第二中学2021-2022学年高三上学期期中数学试题
天津市第二中学2021-2022学年高三上学期期中数学试题(已下线)押全国卷(文科)第20题 圆锥曲线-备战2022年高考数学(文)临考题号押题(全国卷)天津市南开中学2024届高三上学期第三次月考数学试题四川省广安代市中学校2021-2022学年高二上学期第二次月考数学(文)(网班)试题
4 . 已知
,直线
为曲线
在
处的切线,直线
与曲线
相交于点
且
.
(1)求
的取值范围;
(2)(i)证明:
;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86161d12df385eb4cfec8a8a38277fc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e560b5246bb13e0e6bc15a5913eb879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7356730e983351835eb2e750f4f323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f09f29bb529ab9967a275b26e150c5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db551d9fa0c984594e71c295d05c2f23.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6f6cf4ae5f535cdc78120eca2400ed.png)
您最近一年使用:0次
5 . 已知椭圆
的焦点在
轴上,离心率为
,
,
是此椭圆上不同于上顶点
的两点
(1)求椭圆的标准方程;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08df584945b1bc9961138b670327d536.png)
(i)求证:直线
过定点,并求出定点坐标;
(ii)设直线
与抛物线
交于
,
两点,且
,
,
,
从左到右排列,且满足
,设
的面积为
,求
的最小值及此时抛物线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbdea403570229b9d71785778d026adb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求椭圆的标准方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08df584945b1bc9961138b670327d536.png)
(i)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(ii)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c9c87eba774f6bc072663d32d11fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a9fb3a8b8b58ac9772065ca4591625f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6831eebe15fc5b29ef629a850656fe00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b041a570cda8a9885ec594b48e1e48d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f0fbd143133401954fde96e0109015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
名校
6 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffdaf6ce8c6055355f8904726b311df.png)
(1)直接写出曲线
与曲线
的公共点坐标,并求曲线
在公共点处的切线方程;
(2)已知直线
分别交曲线
和
于点
,
.当
时,设
的面积为
,其中O是坐标原点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc873fc03e6e4d3c4ba02f8b1147b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffdaf6ce8c6055355f8904726b311df.png)
(1)直接写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb095e9f5abae37f91650bb8d751a977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9768bacd90ba3b23403f0449c44e822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9768bacd90ba3b23403f0449c44e822.png)
您最近一年使用:0次
2021-11-04更新
|
619次组卷
|
3卷引用:北京市海淀区2022届高三上学期期中练习数学试题
名校
解题方法
7 . 已知函数
,
.
(1)若
,求
的取值范围;
(2)求证:
存在唯一极大值点
,且知
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f035e42df8f6be20fe99d36245395d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beca3a6d6b6f5dbad1d6466c1d3a60b7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8559250e7a91f36fe7a8ec6ce6a1550f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c28ef59d2079f8779315c30f0e45bf9.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dddca059c0e724cff370b46d578ec74.png)
您最近一年使用:0次
2021-10-24更新
|
1343次组卷
|
4卷引用:重庆市育才中学校2023届高三上学期期中数学试题
重庆市育才中学校2023届高三上学期期中数学试题重庆市巴蜀中学2022届高三上学期高考适应性月考(三)数学试题(已下线)第六章 导数与不等式恒成立问题 专题一 两类经典不等式 微点2 两个重要的对数不等式天津市河西区2024届高三下学期第一次质量调查数学试题