1 . 已知函数
.
(1)当
时,若直线
与曲线
相切,求
;
(2)若直线
与曲线
恰有两个公共点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db6dc5779e96494ef7f1c8f973ea86b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/634cfbfa72c819314962cc08fc29ac15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f590ca2bde213675bffe68ed4017f957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
2 . 函数
在
的最大值为m,在
的最大值为n,则以下命题为假命题的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58c65d71e57e6e7697e2f627dcd58583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983fa8d30993077d136d644a4de7a394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca44b51af56d89266c3aba528d8a8d0.png)
A.![]() ![]() ![]() | B.![]() ![]() ![]() |
C.![]() ![]() ![]() | D.![]() ![]() ![]() |
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解题方法
3 . 将足够多的一批规格相同、质地均匀的长方体薄铁块叠放于水平桌面上,每个铁块总比其下层铁块向外伸出一定的长度,如下图,那么最上层的铁块最多可向桌缘外伸出多远而不掉下呢?这就是著名的“里拉斜塔”问题.将铁块从上往下依次标记为第1块、第2块、第3块、……、第n块,将前
块铁块视为整体,若这部分的重心在第
块的上方,且全部铁块整体的重心在桌面的上方,整批铁块就保持不倒.设这批铁块的长度均为1,若记第n块比第
块向桌缘外多伸出的部分的最大长度为
,则根据力学原理,可得
,且
为等差数列.
的通项公式;
(2)记数列
的前
项和为
.
①比较
与
的大小;
②对于无穷数列
,如果存在常数
,对任意的正数
,总存在正整数
,使得
,
,则称数列
收敛于
,也称数列
的极限为
,记为
;反之,则称
不收敛.请根据数列收敛的定义判断
是否收敛?并据此回答“里拉斜塔”问题.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c5abd5f2fc2744d7f706656575b7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12444d6e8d3b097a9d090e6ed06042e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee45219629dd30af171588e646f8b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b78e4a03d4595f14be42054b61dfc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
(2)记数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
①比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6b6c6934eda8f0838d0ba881be2211.png)
②对于无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711c92626a97e6b778b3aa86e663ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ccd4537f4dee2050ade38b972eb9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d1d3b9d14068d68a7cff35ce3e872c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f4691ee07234d7cfc8a21bed1236c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b85738365edd32d8df21b2d36518029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1fd18a909cecbaee7115d6b15631d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d013861990cf331c82eb453416ae31bc.png)
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解题方法
4 . 刻画空间的弯曲性是几何研究的重要内容.用曲率刻画空间弯曲性,规定:多面体顶点的曲率等于
与多面体在该点的面角和的差(多面体的面的内角叫做多面体的面角,角度用弧度制).已知正三棱台
中,
,棱
,
的中点分别为
,
.若该棱台顶点
,
的曲率之差为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d7c958e99bcd9d7f251c19ee3544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/439cf259dd6137aa31bb99244a04ddfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
A.![]() |
B.![]() ![]() |
C.直线![]() ![]() ![]() |
D.多面体![]() ![]() |
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5 . 已知
为坐标原点,矩形
的顶点A,C在抛物线
上,则顶点B的轨迹方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
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6 . 菱形
中,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be3391de7a9edf0b5f4d0104ee35b17d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0449e512918f4b49b373dcda73f4d952.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
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解题方法
7 . 如图所示的几何体是由圆锥
与圆柱
组成的组合体,其中圆柱的轴截面
是边长为2的正方形,圆锥的高
,M为圆柱下底面圆周上异于A,B的点.
∥平面
;
(2)若
,求直线
与平面
所成角的正切值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a8c34f622f1b979feed5ae6ae5d0e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0a4f38420bb9215dbc9c875b755838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a55a6b8045f2d6429ac49997c1124a25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08452588675f76da2f8d31387b3a8224.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b10c2bc31ab83c89237b93159ae64c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08452588675f76da2f8d31387b3a8224.png)
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解题方法
8 . 已知四面体有两个面是边长为2的正三角形,另外两个面是直角三角形,则该四面体的体积等于__________ .
您最近一年使用:0次
解题方法
9 . 设A,B为椭圆C:
的短轴端点,P为椭圆上异于A,B的任意一点,D在直线
上.
(1)求直线
,
的斜率的乘积;
(2)证明:
;
(3)过右焦点F作x轴的垂线
,E为
上异于F的任意一点,直线
交C于M,N两点,记直线
,
,
的斜率分别为
,
,
,是否存在
,
,
的某个排列,使得这三个数成等差数列?若存在,加以证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6922c5dbeead5d1225b2933e92719f2f.png)
(3)过右焦点F作x轴的垂线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
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解题方法
10 . 已知圆的内接四边形
中,
,
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f89deb952f57f4b3fa4887b098b7b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3a771c5a24180b7d5c5db0f5179079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c9c9357f6e618f149423a945a68ddf.png)
A.-3 | B.![]() | C.![]() | D.3 |
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