解题方法
1 . 已知正四面体
的棱长为2,M,N分别是棱
,
的中点,过M、N作正四面体
的截面
.有下列结论,其中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.异面直线![]() ![]() ![]() | B.![]() |
C.若截面![]() | D.截面![]() |
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2 . 已知函数
,其中
表示
,
中的最大值,若函数
有3个零点,则实数
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b532b68bfc793ca4826283d97458ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385e1459ada24f66206d0de24a85ad0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
3 . 英国数学家泰勒(B.Taylor,1685—1731)发现了:当函数
在定义域内n阶可导,则有如下公式:
以上公式称为函数
的泰勒展开式,简称为泰勒公式.其中,
,
表示
的n阶导数,即
连续求n次导数.根据以上信息,并结合高中所学的数学知识,解决如下问题:
(1)写出
的泰勒展开式(至少有5项);
(2)设
,若
是
的极小值点,求实数a的取值范围;
(3)若
,k为正整数,求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ba62322394a513a9e60536e424f112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c875ad8fafc41d5c82baf23bb5e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd370c3b127fbdb77b6e5c40318328d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad040ae0fab73f5dd7b1af48cd3b5f93.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a923c6ef8e8a289acf935ca73c92a28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf90a3d768f2a8ff0ede2f973d1dad1.png)
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2卷引用:贵州省遵义市2024届高三第三次质量监测数学试卷
4 . 若数列
和
的项数均为
,则将数列
和
的距离定义为
.
(1)求数列1,3,5,6和数列2,3,10,7的距离;
(2)记A为满足递推关系
的所有数列
的集合,数列
和
为A中的两个元素,且项数均为
.若
,
,数列
和
的距离
,求m的最大值;
(3)记S是所有7项数列
(其中
,
或1)的集合,
,且T中的任何两个元素的距离大于或等于3.求证:T中的元素个数小于或等于16.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58eb2bc16ca7ba6db8792eec6e2b48c0.png)
(1)求数列1,3,5,6和数列2,3,10,7的距离;
(2)记A为满足递推关系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23093a3f4c23494a943e3957596fee92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2865594c03cd3cfcbf3216cdbf08fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77cb4aa359781e637bd2232813fa8a24.png)
(3)记S是所有7项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d7457bc36b80660dc03b668674f065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bd42f8e3f220a7b1c6f6945e73bc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c458592ba2d5ddd559b8720438a8fe.png)
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解题方法
5 . 已知椭圆
的左右焦点为
,
,P是椭圆C上的动点,
的最大值为8,当
时,
.
(1)求椭圆C的标准方程;
(2)点
,若点M,N在椭圆C上,且直线
,
的斜率乘积为
,线段
的中点G,当直线
与y轴的截距为负数时,求
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.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/560510300ddfc5c893e0d4123bbf9f22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde69214438f3a720c8094e886eb31dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dccf31e2e06794301c8dff7939521ce.png)
(1)求椭圆C的标准方程;
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1bd72b6e698a649d551a0ec50e3b2a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b09bf6ba623953df55eb869b2b363e39.png)
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6 . 已知
,则使不等式
能成立的正整数
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc66afc1e6e40f45ffeea65fb2c925bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddac9d23ae90a2c3ad1225bb2388562d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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|
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3卷引用:贵州省贵阳市清华中学2024届高三下学期5月高考临考预测数学试题
7 . 已知函数
.
(1)讨论
的单调性;
(2)若对任意的
,存在
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adab31dba50d0320c510a21e49d4913c.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca3c74f5e721d8e3277c7757fb9d657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 差分密码分析(Differential Cryptanalysis)是一种密码分析方法,旨在通过观察密码算法在不同输入差分下产生的输出差分,来推断出密码算法的密钥信息.对于数列
,规定
为数列
的一阶差分数列,其中
;规定
为
的二阶差分数列,其中
.如果
的一阶差分数列满足
,则称
是“绝对差异数列”;如果
的二阶差分数列满足
,则称
是“累差不变数列”.
(1)设数列
,判断数列
是否为“绝对差异数列”或“累差不变数列”,请说明理由;
(2)设数列
的通项公式
,分别判断
是否为等差数列,请说明理由;
(3)设各项均为正数的数列
为“累差不变数列”,其前
项和为
,且对
,都有
,对满足
的任意正整数
都有
,且不等式
恒成立,求实数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2308a0aeed12a4353b098ae06e04af9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a3263d776109ee6034a6ee97b37d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de1b87726fc455bda6b57a6bbf945370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e274217ecbdfeea729eaa317359e77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eda2ec94bfc822d28635c095bdb758f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b3ffa99683b52161e653e1235cb6f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65e9e65ce496d6a1f8be6d7d0af1bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89d7ba76ae33842a28eed52601094254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895bbc9662386113650ad8a168eff301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/979d34c8d77abf2ebbb3e8e1f88776c3.png)
(3)设各项均为正数的数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b78297a65e7fad69635b19928ecc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19123452d0581bfafcabd85c28f598a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a35f3fd5b7c33cb9c9550636b933157a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0da40c1842335a4c83f5be6a8b85a382.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefdf7c484fe016725e6389dc3f5b324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f4057fbc6a2084aa1a2ad141b1161f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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9 . 已知函数
,且
与
轴相切于坐标原点.
(1)求实数
的值及
的最大值;
(2)证明:当
时,
;
(3)判断关于
的方程
实数根的个数,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e1375088563294adc1b57cb48833bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06d4aa6849bbb8b543a0b361e1ebb0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d541585c3e7895f814e6cb37c57452d.png)
(3)判断关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cf3b13382a1f1dfeb7deebb3f5e925.png)
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3卷引用:贵州省毕节市织金县部分学校2024届高三下学期一模考试数学试题(一)
名校
10 . 如图,在三棱台
中,
在
边上,平面
平面
,
,
,
,
,
.
;
(2)若
且
的面积为
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7d82423b6f211a7ac51a850b55e73a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa18c2a78c400c80a5760743f31771c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a309d190802e8a90b421174da5cfc72a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e673ef2d48215ca84a48377f17d6df00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8439d059d08e4ee524b234f3f490aaa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c672f693a7e75a7bae4936dcb1920430.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd2e870c95b1ed54b281f93e683578bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2ca820a456491348e72587e4fe10bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
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