1 . 已知正项数列
满足
且
.
(1)求证:数列
为等比数列,并求数列
的通项公式;
(2)证明:数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd78271826e0a5f74cc0540c3ed1802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14835bf3f00139ccec0694d0924db795.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1302abaebc9df026c2a83291063e83b4.png)
您最近一年使用:0次
2 . 已知函数
.
(1)求
的最小值;
(2)判断
在
上的单调性,并根据定义证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6f4c2d346c9f8148d832f6bc9a57699.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d6243e93c41978871cb23d8e66148d.png)
您最近一年使用:0次
2024-01-17更新
|
408次组卷
|
5卷引用:贵州省黔东南州2023-2024学年高一上学期期末检测数学试题
3 . 已知离心率为
的椭圆
与x轴,y轴正半轴交于
两点,作直线
的平行线交椭圆于
两点.
(1)若
的面积为1,求椭圆的标准方程;
(2)在(1)的条件下,记直线
的斜率分别为
,
,求证:
为定值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(2)在(1)的条件下,记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.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/b4757181824e15e0f21e5bdd55448783.png)
您最近一年使用:0次
2023-10-07更新
|
1994次组卷
|
5卷引用:贵州省黔东南州从江县2024届高三上学期11月检测数学试题
贵州省黔东南州从江县2024届高三上学期11月检测数学试题甘肃省永昌县第一高级中学2023-2024学年高三上学期10月第一次数学月考试题 (已下线)考点16 解析几何中的定值问题 2024届高考数学考点总动员【练】湖北省武汉市汉阳区武汉情智学校2023-2024学年高二上学期11月期中考试数学试题(已下线)专题23 椭圆的简单几何性质10种常见考法归类(3)
解题方法
4 . 已知函数
.
(1)解不等式
;
(2)当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f54a0c07847bb5a711881d4ac2bac957.png)
(1)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd5e026a565c24617edc36f82fd85e63.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94ae11e65a5c125d804bf537c419efc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fccad0a93acd2f36bc78d8a8f3e04e5b.png)
您最近一年使用:0次
2023-12-15更新
|
53次组卷
|
2卷引用:贵州省黔东南自治州镇远县文德民族中学校2022届高三上学期期末数学(理)试题
名校
5 . 已知函数
在
处的切线为
轴.
(1)求实数
的值;
(2)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6a5d7726fe6c16df9f230cc4954f59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec72ca557aa4229ee871628ffcf0d8a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78f7b93cc1e59257a15b904ca84983a.png)
您最近一年使用:0次
解题方法
6 . 如图,在四棱锥
中,侧面
是正三角形,且与底面
垂直,已知底面
是菱形,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/77e2ca8e-b809-4782-966c-ef5b7ee70557.png?resizew=178)
(1)求证:
;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03977f376d19e1ba2e50881e511e3e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/11/77e2ca8e-b809-4782-966c-ef5b7ee70557.png?resizew=178)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44f4120c94cb7176dc31fcac387b32e.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfe67036b4671b5d2a5c55b48c4d3bb9.png)
您最近一年使用:0次
7 . 如图,在正方体
中,
.
(1)求证:
平面
;
(2)求证:平面
平面
;
(3)求直线
和平面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/11/17b4bf83-6b29-40b7-a4ec-b71fd7074d9b.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb04914c4e8fb3483da44c67fe1809f.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f5e22b37cea8a05fa13f85414c7c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb04914c4e8fb3483da44c67fe1809f.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb04914c4e8fb3483da44c67fe1809f.png)
您最近一年使用:0次
名校
8 . 如图,在四棱台
中,
为
的中点,
.
平面
;
(2)若平面
平面
,
,当四棱锥
的体积最大时,求
与平面
夹角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/730b40d2a7bb0d6e460c0f0795a167e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ee25460ee82d00c603c36f209bd52f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b15365ce57a7faf8812afef900e515b.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14ed361b17653d40a5bd1d66a915594.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
您最近一年使用:0次
2024-05-29更新
|
1084次组卷
|
3卷引用:贵州省凯里市第一中学2024届高三模拟考试(二模)数学试题
解题方法
9 . 已知点
在抛物线
上,点
在第一象限,过点
且与
相切的直线
与
轴交于点
,与
轴交于点
.
(1)证明:
是
的中点.
(2)过点
作
的垂线交
于另一点
,且
,求
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd161de7800e9d69a0bce282b6011e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
10 . 如图,在多面体
中,四边形
为菱形,
平面
,
,
,
,
.
平面
;
(2)试问线段
上是否存在一点
,使得平面
与平面
夹角的余弦值为
?若存在,请判断点
的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3139e28714bfc3d5d875d78dd245d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e343510d82161bb1da2f17403f5d1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4280be91682e5d8a0d0704190319bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac7823e6a47ed42d8da12efbf61fe5af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
(2)试问线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cdb19af3fe72be6542fb0d94f285b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2024-03-19更新
|
769次组卷
|
2卷引用:贵州省黔东南州2024届高三下学期模拟统测(二模)数学试题