名校
解题方法
1 . 对于数集X={-1,x1,x2,
,xn},其中
,n ≥ 2,定义向量集
,若对任意
,存在
,使得
,则称X具有性质P.例如{-1,1,2}具有性质P.
(1)若x > 2,且{-1,1,2,x}具有性质P,求x的值;
(2〉若X具有性质P,求证:1 ∈X ,且当xn >1 时,x1= 1;
(3)若X具有性质P,且x1= 1 ,x2 =q (q为常数),求有穷数列x1,x2,
,xn的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0040b12a13d03d5f1c6c1f80ac0365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac4d197ead9c1bc27b05aedac23ad79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c122d308af408739c2717376e932122d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c6bb4424eb1e5ab02b8ac83fd6ad10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8de3dabcc3150fd539ac97718ba10c5.png)
(1)若x > 2,且{-1,1,2,x}具有性质P,求x的值;
(2〉若X具有性质P,求证:1 ∈X ,且当xn >1 时,x1= 1;
(3)若X具有性质P,且x1= 1 ,x2 =q (q为常数),求有穷数列x1,x2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
您最近一年使用:0次
2021-08-29更新
|
542次组卷
|
6卷引用:北京市第十五中学2017-2018学年高三上学期期中考试数学理试题
名校
2 . 已知集合
是满足下列性质的函数
的全体:在定义域内存在实数
,使得
.
(1)判断函数
(
为常数)是否属于集合
;
(2)若
属于集合
,求实数
的取值范围;
(3)若
,求证:对任意实数
,都有
属于集合
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55aa87b1d7ab2a912313eaee2a244263.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa279306676cbc09ddcb9ff6f991a07a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/160fc027e9c1023c5203595d4b88c05e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd337b3fc9e3e34afc15aef70414629a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2020-03-02更新
|
742次组卷
|
3卷引用:上海市上海中学2019-2020学年高一上学期期末数学试题
3 . 已知直线与抛物线交于两点.
(1)求证:若直线
过抛物线的焦点,则
;
(2)写出(1)的逆命题,判断真假,并证明你的判断.
(1)求证:若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/749b17e02ac5325dcfcac745a51b5170.png)
(2)写出(1)的逆命题,判断真假,并证明你的判断.
您最近一年使用:0次
4 . (1)若圆
的方程是
,求证:过圆
上一点
的切线方程为
.
(2)若圆
的方程是
,则过圆
上一点
的切线方程为_______ ,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3503d330608e7138d1b529aba4512fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d340bd3f078b9261238d4fe59f1473c1.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e885d3743ae3d9f0fbd740b75f900083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
您最近一年使用:0次
2020-02-29更新
|
221次组卷
|
2卷引用:上海市七宝中学2019-2020学年高二上学期期末数学试题
名校
解题方法
5 . 已知函数
,
.
(1)当
时,求函数
在
上的单调性;
(2)是否存在实数
,使得函数
在
上的最小值为3,若存在,求出
的值,若不存在,请说明理由;
(3)当
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b8670b8c6c3d9d7b72094c98eb719be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94c4236a438856166b1f1d1b954f7d01.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c84b49231d0344d0813a7bbd2acdaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7863b54185da5a3f1a765e1aa0577e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab5e0524def52baf53480b8726784ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/725173c99b6fbb958cdab101569985dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/221d40ea04298c5569cf8b2708972b11.png)
您最近一年使用:0次
6 . 如图,在四棱锥
中,底面
是平行四边形,
,
底面
,
,E,F分别为
,
的中点,点M在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/456b4198-b369-44ed-9d55-fc27b1e44a9b.png?resizew=165)
(1)求证:面
面
;
(2)若M为线段
的中点,求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319536a5b0d3f94d4b1a495c3b19d79b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3b8822bbb5ba39c90550ac277cfe88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/456b4198-b369-44ed-9d55-fc27b1e44a9b.png?resizew=165)
(1)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e83401c0e1468e1f3385bdd68d3dd21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若M为线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce6c0e9de83f2e64ae33609fc08459d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
7 . 已知
,数列A:
,
,…
中的项均为不大于
的正整数.
表示
,
,…
中
的个数(
).定义变换
,
将数列
变成数列
:
,
,…
其中
.
(1)若
,对数列
:
,写出
的值;
(2)已知对任意的
(
),存在
中的项
,使得
.求证:
(
)的充分必要条件为
(
);
(3)若
,对于数列
:
,
,…
,令
:
,求证:
(
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce056bb311610344f135cb4556ec077c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9e5dfcc28321b563a8012ec2899c502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e916da5bbc4b0ee4a28b8cac0441569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40451e0f90ba4df0cb35143b93303a22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a9157ebffc000886668360981197041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c213b8556a744796d802db4e58985a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/759a1cbe003f428408437339560e3266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ee2879f90de81ba04d18aa6079de35.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e984320c35fd2f65f72df993cb2c97a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1cb1d423ec1930011e4c7ed79fb9a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6931690445142df14a6f487d8fff4a7e.png)
(2)已知对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab1e6771cf5aa28cf594514258ead70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ae1522a36768618f7ddaf74abbb7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c85be1194188e0a726d343b1c9237f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca9e69e2b87edb1044bc902bf8f0b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4043f483f8ab44ce5895d8c85dd30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e80d145b01074362d1e4ae6c6391326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029c1b13246250173b74f56d7007269e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a64ed93e3ac6fae4ec774bc4e90cb05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f7d7a031e551e9f6f7de0351e1380d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0850369056d53c0f7758ecd59db920d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48b26484e0328c0fc9c29b774aef4287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4043f483f8ab44ce5895d8c85dd30.png)
您最近一年使用:0次
2020-03-04更新
|
373次组卷
|
3卷引用:【区级联考】北京市东城区2019届高三第二学期综合练习(一)数学(理)试题
名校
解题方法
8 . 已知定义在
上的函数
满足:①对任意
,有
.②当
时,
且
.
(1)求证:
;
(2)判断函数
的奇偶性,并加以证明;
(3)解不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd384d86840b7b158af41f56fe29c7d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee2947fc3fa97440c015e00f14c6218.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104375baf5cef5eb92cfc7cf13b80193.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf6aaa7278470b100581aae5d219373.png)
您最近一年使用:0次
名校
9 . 在直角坐标平面
上的一列点
,简记为
.若由
构成的数列
满足
,其中
为方向与
轴正方向相同的单位向量,则称
为
点列.
(1)判断
,是否为
点列,并说明理由;
(2)若
为
点列,且点
在点
的右上方.任取其中连续三点
,判断
的形状(锐角三角形、直角三角形、钝角三角形),并予以证明;
(3)若
为
点列,正整数
,满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c13b920ec4a33103954c68daa7644ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7836415e9b77334eee27c0d497ca5ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b7daef66f5d193befe316e6a9df2bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821a7c2e810ef18a2ee78f3722f03c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9b7813755384e0b6044fe296d7c6029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2a09e3d201f7699e8d480c768e34696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6edc135bb869e8e8dd68b711d147e368.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621604766ddd141c86e37da5e71aef26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06dfbe171fd6d47d6b8ab101b62ac0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ada35c9021498f44a4c7cb9efd058bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e71cb7bfc09205b70196aeadad57439.png)
您最近一年使用:0次
2020-06-26更新
|
580次组卷
|
7卷引用:上海市奉贤中学2018-2019学年高二上学期10月月考数学试题
名校
解题方法
10 . 已知函数
对任意实数x,
,满足条件
,
且当
时,
.
(1)求证:
是R上的递增函数;
(2)解不等式
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54dad48527a47eab4a5916ab0421cc71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb984de1cd94e043ebeb09dddae6c84a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78165f7cd39dc85a48ca9794290c626c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/736d35fb5b436cd822304eb8efdcefd3.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
(2)解不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096651d50d2f45f4fa9b9e318253cade.png)
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2020-02-29更新
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1124次组卷
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5卷引用:江苏省淮安市淮阴中学2019-2020学年高一上学期期中数学试题