1 . 已知函数
,(
).
(1)分别计算
,
的值.
(2)由(1)你发现了什么结论?并加以证明.
(3)利用(2)中的结论计算
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb6d1989232018220bca0a1e84ac83e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
(1)分别计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b2cb4e04d259f4f28a5ab1b31f7c966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1ca7d59338a54935cab36d7fee29f5.png)
(2)由(1)你发现了什么结论?并加以证明.
(3)利用(2)中的结论计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32961d0d475d243c06ab5e2ab29eae22.png)
您最近一年使用:0次
2023-04-02更新
|
433次组卷
|
2卷引用:重庆市育才中学校2023-2024学年高一上学期拔尖强基联合定时检测(一)数学试题
名校
2 . 已知平面向量
不共线,由平面向量基本定理知,对于该平面内的任意向量
,都存在唯一的有序实数对
,使得
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/21b0c195-8bde-44b9-b7f2-f7aed4065d2e.png?resizew=166)
(1)证明:
三点共线的充要条件是
;
(2)如图,
的重心
是三条中线
的交点,证明:重心为中线的三等分点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/087f8cb64adc6f6e5767b90529ad69ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91174b2336306191ba275a87864172b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7dccdea80bdc0e9b2cddda1b79cbba9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/21/21b0c195-8bde-44b9-b7f2-f7aed4065d2e.png?resizew=166)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b11b45b1ae99a58e5aac679974dabcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
(2)如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c42f73b6b4cd5308071e6bedb83049.png)
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名校
解题方法
3 . 已知正方形
的边长为2,点
分别是边
的中点,沿着
将
,折起,使得点
重合为一点
,得到一个三棱锥
,点
分别是线段
的中点,在折起后的图形中:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/7b087ae0-a307-4c36-96f9-1a32e3caae8a.png?resizew=273)
(1)求证:平面
平面
;
(2)求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ae536809b1161fd4e83fdc7f42be96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11a595799a9cbcc3e9d8cf8f0c6615f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57e7e167f74e69ed342904cc848da6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f823f65ec0f4c28327c7ecbc4128d182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/929ee53fdccf52c453b2bddf772d9b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50c548a33e9888a9bf2d455a5c59dd62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45e389a6feef9e81b3804a451144287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/551bf13322d8786dfa2edd4b038318c1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/7b087ae0-a307-4c36-96f9-1a32e3caae8a.png?resizew=273)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dffd6793219dec53303a4512f0c0fa97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a3a62ac6583372ffe2ce0d415273a47.png)
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4 . 在数列
中,
,
.
(1)证明:数列
为等比数列;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366dfedff1a1a96ec27650375b680059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c02634d8fbae8319b26f6f3f165d5a0.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4085913b1c322004d417a396f735e044.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0496f142d8ae5acb06e83526eaa3ef87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
您最近一年使用:0次
2023-01-17更新
|
1682次组卷
|
2卷引用:重庆市杨家坪中学2022-2023学年高二下学期第一次月考数学试题
名校
解题方法
5 . 已知椭圆
过点
,且离心率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆E的标准方程;
(2)若直线l与椭圆E相切,过点
作直线l的垂线,垂足为N,O为坐标原点,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b54b9cf95418bc3dce6e4c698b9907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆E的标准方程;
(2)若直线l与椭圆E相切,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c9dcfd9f4c5298035870cb88a34169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291a0231b8630f8eda4245105ef7c38b.png)
您最近一年使用:0次
2023-03-29更新
|
2197次组卷
|
7卷引用:重庆外国语学校(四川外国语大学附属外国语学校)2022-2023学年高二下学期5月月考数学试题
名校
6 . 已知向量
,函数
.
(1)求函数
的单调增区间和对称轴;
(2)若关于
的方程
在
上有两个不同的解,记为
.
①求实数
的取值范围;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8932c215fa26c494f60f53b31c9ab008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e7b2150ed88d3ffdec3d142617eacf.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3b4874cf36b6082ba4d539ff3ee69a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c9aeed3c8c5a04e48d011c607f9142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2f9f83b1c9ef035eaafbe12b8dd5cf.png)
您最近一年使用:0次
名校
7 . 双曲函数是一类与常见的三角函数类似的函数,最基本的双曲函数是双曲正弦函数和双曲余弦函数(历史上著名的“悬链线问题”与之相关).其中双曲正弦函数:
,双曲余弦函数:
(
是自然对数的底数
).这两个最基本的双曲函数具有如下性质:
①定义域均为
,且
在
上是增函数;
②
为奇函数,
为偶函数;
③
.
(1)请证明双曲正弦函数
在
上是增函数;
(2)若存在
,关于
的方程
有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4285cf0589158ab4a30f1fef52a3628f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2a73959e07bb1d8a335151521b99f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa9b12852f286c2d26734a31b3b08c8.png)
①定义域均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcb4ebafc43af0d7298402e793f27665.png)
(1)请证明双曲正弦函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee4b3fef47212d2ac45ccdbc7620c4d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f80c76560aea27504587f19fd6ccba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2022-12-20更新
|
357次组卷
|
2卷引用:重庆市育才中学校2022-2023学年高一上学期12月月考数学试题
名校
解题方法
8 . 已知函数
.
(1)求函数
的单调区间和最大值;
(2)设函数
有两个零点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/493c5747bc6d9445fe2afe60a3b5bec5.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147646cd9e3edaf051ee2acdf6737c33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
您最近一年使用:0次
2023-03-12更新
|
1206次组卷
|
4卷引用:重庆市杨家坪中学2022-2023学年高二下学期第一次月考数学试题
名校
9 . 如图,在三棱柱
中,
平面ABC,D,E,F分别为
,AC,
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/18/10aa192c-2b71-4d70-a7bf-16c280aa14f1.png?resizew=169)
(1)求证:AC⊥平面BEF;
(2)求点D与平面
的距离;
(3)求二面角
的正弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1efa2b0018617bd579875185dafca39a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9d5815dc775d5a5810fff0b016a8d5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/18/10aa192c-2b71-4d70-a7bf-16c280aa14f1.png?resizew=169)
(1)求证:AC⊥平面BEF;
(2)求点D与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bba99277e38f8d9f817a9d7db8198219.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59b1f7689bff6644bfdeb9e36feb163.png)
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名校
10 . 如图,在直三棱柱ABC-A1B1C1中,AA1=AB=AC=1,AB⊥AC,M,N,Q分别为CC1,BC,AC的中点,点P在线段A1B1上运动,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/7d32007d-3f04-41ce-86bf-06121356e06a.png?resizew=222)
(1)证明:无论λ取何值,总有AM⊥平面PNQ;
(2)是否存在点P,使得平面PMN与平面ABC的夹角为60°?若存在,试确定点P的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c019910d3e5bec7e0f6f9a6e206a92.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/7d32007d-3f04-41ce-86bf-06121356e06a.png?resizew=222)
(1)证明:无论λ取何值,总有AM⊥平面PNQ;
(2)是否存在点P,使得平面PMN与平面ABC的夹角为60°?若存在,试确定点P的位置;若不存在,请说明理由.
您最近一年使用:0次
2022-09-09更新
|
914次组卷
|
8卷引用:重庆实验外国语学校2022-2023学年高二上学期九月检测数学试题