解题方法
1 . 已知双曲线C:
(
,
)的右焦点为F,过F的直线l与x轴垂直,且与C交于A,B两点,若
与
的夹角为
(O为原点),则双曲线C的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
A.![]() | B.2 | C.![]() | D.![]() |
您最近一年使用:0次
2 . 已知函数
(
,
)的部分图象如图所示,图象与y轴的交点为
,若
(
),且
在
上有两个极值点,则a的取值范围是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/81830bc4-4b8b-41f3-9b51-d4aef36cecb3.png?resizew=132)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3458e4015b9fa3549126d4b93d1c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad57bb09b32ff941dde57f000b82fd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a791345dd42a1504a85be8325d88e1f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd11639b2de87351909e221f7bd9b239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23efa380a58dc9663ba06dc249ce721.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/81830bc4-4b8b-41f3-9b51-d4aef36cecb3.png?resizew=132)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
3 . 如图,在四棱锥
中,平面
平面
,
,
,
,
,
,点O为
的中点.
(1)若点E为
的中点,求证:
;
(2)设四棱锥
的体积为
,点M为底面四边形
内一点(包括四边形边上的点),且直线
与底面
所成的角为
,求直线
与平面
所成角的正弦值的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0453cfd7e92bf7746a88280b9e7b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62974d34de3a12418d6b700420afd1b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa6ea683971fa8b6299d7aab6d04092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/3/d90ec7b9-6678-4249-8bf6-1945f0b2d78b.png?resizew=171)
(1)若点E为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d4441a872d82bf3b21461c8d9786cc.png)
(2)设四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb57d84f9bbcb3e30d4ce7e2e1e8604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d9792485ccd1ba479ceba6397c15ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479af92937acd790f85e3035afad897d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d9792485ccd1ba479ceba6397c15ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27d39f37441ee55dbc8f1a6ca199a66b.png)
您最近一年使用:0次
4 . 已知
,且
有两个极值点
,
(
).
(1)求a的取值范围;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d8ab90e6781d6c34fac86e63bcbc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
(1)求a的取值范围;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc68b2bb537e009910cebca169117866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8dc531505ec45b8eb8ae4fad88d69e8.png)
您最近一年使用:0次
5 . 已知圆锥的顶点为P,底面圆心为O,AB为底面直径,
为直角三角形,
,点C在底面圆周上(不与A,B重合),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2cc5f8cec8c498aa12c99c04e1c97d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
A.三棱锥![]() ![]() |
B.当三棱锥![]() ![]() |
C.存在点C,使得平面PBC与底面ABC夹角的正弦值为![]() |
D.平面PBC与平面PAC夹角的余弦值的取值范围为![]() |
您最近一年使用:0次
解题方法
6 . 已知函数
在
上不单调,则a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae54899fef586a618b6f19f5dd5ab20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
解题方法
7 . 若
为奇函数,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa10e5ed6e810293b194bc3cec0f276.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.![]() | B.3 | C.0 | D.1 |
您最近一年使用:0次
解题方法
8 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e888ea14da893971e13858945bf0cd.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c49a9bae6637cb8680f67ec1d1a240fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e888ea14da893971e13858945bf0cd.png)
您最近一年使用:0次
解题方法
9 . 已知椭圆C:
(
)的左、右焦点分别为
,
,过
的直线l与椭圆C交于P,Q两点,与y轴交于点G.
(1)已知过原点且与l平行的直线
与椭圆C交于点A,B,求证:
;
(2)若椭圆C的离心率为
,且
,
,问
是否为定值?若是,求
的值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
(1)已知过原点且与l平行的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624bf696e787cad7ce0f61b0404d6ace.png)
(2)若椭圆C的离心率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1996ba299a5a938593f8775404bdc35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d155673e6c19aca7c4b064d6a79557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a19bc9c7083b1e9538337a3038712896.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a19bc9c7083b1e9538337a3038712896.png)
您最近一年使用:0次
10 . 已知
的内角A,B,C的对边分别为a,b,c,
的面积为
,
为
的角平分线,且交
于点D,
.
(1)若
,求
的周长;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f83dbfddc6f98548699ed581e8c8608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1da58573adede69984f16560dee854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43efdcf995d5c26d1075de445a986e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03005d17bf564371ad29fea41f5c650.png)
您最近一年使用:0次