名校
1 . 已知函数
在点
处的切线方程为
.
(1)求
、
的值:
(2)求函数
的单调区间;
(3)令
,若函数
的极小值小于
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6537a3b788e62a9a81e937cf76f81f90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1d8d5cea065075fe50706abe3ae802.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6dae29376f189bd1cc275999bfc0915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95b6be4554f03bf496092f1acdfbb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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3卷引用:北京市清华附中2022-2023学年高二下学期期末数学试题
北京市清华附中2022-2023学年高二下学期期末数学试题【北京专用】专题11导数及其应用(第三部分)-高二上学期名校期末好题汇编(已下线)第09讲:一元函数的导数及其应用 (必刷7大考题+7大题型) -2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)
2 . 给定正整数n,记S(n)为所有由2n个非负实数组成的2行n列的数表构成的集合.对于A
S(n),用
,
分别表示的第i行,第j列各数之和(i=1,2;j=1,2,...,n).将A的每列的两个数中任选一个变为0(可以将0变为0)而另一个数不变,得到的数表称为A的一个残表.
(1)对如下数表A,写出A的所有残表A',使得
;
(2)已知A
S(2)且
(j=1,2),求证:一定存在A的某个残表A'使得
,
均不超过
;
(3)已知A
S(23)且
(j=1,2,...,23),求证:一定存在A的某个残表A'使得
,
均不超过6.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02d44492b51b0e08208fdc0d1707025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469ffe912a03e649a7876c9e4a8d623b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b8db2510161ab72e498d0c03e1642d.png)
(1)对如下数表A,写出A的所有残表A',使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13e85642202627ac8c75fdabefd111ec.png)
0.1 | 0.1 | 1 |
0 | 0 | 0.1 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02d44492b51b0e08208fdc0d1707025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012c4214a90f64342b01baa95415b08f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0d291ac1dd64c77ae386ebd9edea97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9ae6fe0a2b338225e7bbe1267fde97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
(3)已知A
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a02d44492b51b0e08208fdc0d1707025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012c4214a90f64342b01baa95415b08f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0d291ac1dd64c77ae386ebd9edea97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9ae6fe0a2b338225e7bbe1267fde97.png)
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3 . 已知函数
,若函数
在点
处的切线方程为
.
(1)求
,
的值;
(2)求
的单调区间;
(3)当
时,若存在常数
,使得方程
有两个不同的实数解
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9cc876a2a8d1461b737861169248ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9355031ea0b2dc9cef3777621bc6d38.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976d18a5396ba232f0aa38d136f1d749.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/03ca13a93b5f401c0d39ba52b0cffcb0.png)
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4 . 已知函数
,取点
,过
作曲线
的切线交y轴于
,取点
,过
作曲线
的切线交y轴于
......依此类推,直到当
时停止操作,此时得到数列
.给出下列四个结论:①
;②当
时,
;③当
时,
恒成立;④若存在k∈N*,使得
,
,…,
成等差数列,则k的取值只能为3.其中,所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/722bf15521a0167d2946e7a3c5ba293c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5614dfcc099de673b208bb69c340bfdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994a73686deb355bd5dc11276e481fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64263fe2ca48e694c87496d61e63fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f15b10c362800032976abea026b0d433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808055c60d55f08405cf5182ca403c99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bf1a283bc365a5bda7cd91e76766bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74e5ced14046ffd5c9e4e8b3405f5f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab2b74474c95838de5ca565e7708832.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74e5ced14046ffd5c9e4e8b3405f5f27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d143a396bb10a9f72d9fe1adc6d8f67.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/5f255d0395fba51ca2d44293cca42e0a.png)
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解题方法
5 . 已知函数
在区间
上是单调函数,则正数
的一个取值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b231a5810847532d08dad2c92f36e081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4b49d457a11e6ddb789f5027dcd1491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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|
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2卷引用:北京市海淀区清华大学附属中学2022-2023学年高一下学期期末考试数学试题
名校
解题方法
6 . 已知复数
的模为5,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b23af12fe08e6be5d5879fe591ccab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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4卷引用:北京市海淀区清华大学附属中学2022-2023学年高一下学期期末考试数学试题
北京市海淀区清华大学附属中学2022-2023学年高一下学期期末考试数学试题【北京专用】专题11复数(第二部分)-高一下学期名校期末好题汇编(已下线)第02讲 7.1.2 复数的几何意义(1)-【帮课堂】(人教A版2019必修第二册)(已下线)10.1.2复数的几何意义-同步精品课堂(人教B版2019必修第四册)
名校
解题方法
7 . 在复平面内,复数
对应的点位于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ff9bb0405759b1454452a471bda51f.png)
A.第一象限 | B.第二象限 | C.第三象限 | D.第四象限 |
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8卷引用:北京市海淀区清华大学附属中学2022-2023学年高一下学期期末考试数学试题
解题方法
8 . 在复平面内,
是原点,向量
对应的复数是
,向量
对应的复数是
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58fc620efc80915b474b31fdd73647c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9df77dc0d9ae32a07bd011af9928175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2f25dfa0e743fdef251ccd5678afb3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2f6f85a901030a832853f848dbf111d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/060e2f828634e15b4f9db3b2d02937aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
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6卷引用:北京市丰台区2022-2023学年高一下学期期末考试数学试卷
北京市丰台区2022-2023学年高一下学期期末考试数学试卷(已下线)第六章 复数与平面向量 专题2 有关复数的几何意义(已下线)专题02 平面向量的坐标运算及平行、垂直关系4种常考题型归类-《期末真题分类汇编》(北京专用)(已下线)专题03 复数5种常考题型归类-《期末真题分类汇编》(北京专用)【北京专用】专题11复数(第二部分)-高一下学期名校期末好题汇编(已下线)专题2.1复数的概念-重难点突破及混淆易错规避(人教A版2019必修第二册)
名校
解题方法
9 . 已知集合
,若对于任意
,存在
,使得
成立,则称集合
是“
集合”.给出下列5个集合:
①
;②
;③
;
④
;⑤
.
其中是“
集合”的所有序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b392b98ebc75d96d89422ac4f17d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355c6295d218cd43e397064c7dcc19c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d40d7bb263b5d955f45b08fc18b102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da3ff6f17be99ec311610efa08ba002.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96d74469bc5ecbf963d3394ca985d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e12a562293694bbd5234fe005d8f3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d0d6a7a76186e89d6dffafe3cca5da.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed141072fbdd94f18b387c9bf0c6ac5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24f94ac7d8e8d0731fe9b1b5db4b09c.png)
其中是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
A.②③ | B.①④⑤ | C.③⑤ | D.①②④ |
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3卷引用:北京市第五中学2022-2023学年高二下学期期末检测数学试题
解题方法
10 . 已知函数
.
(1)若对任意
时,
成立,求实数
的最大值;
(2)若
,求证:
;
(3)若存在
,使得
成立,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2419b2560cb5493ee0d187ddc265d5cb.png)
(1)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66692ec49a458f9e48c7315d03dfc37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5931095eb29d9d6b55ed9fa32a4ef1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e312eca38032174f9739126b81d012.png)
(3)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5f4aadc17b6d5c9760a75fab7fb760.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3628078fad0d12a8bb238314a6a8fb6e.png)
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4卷引用:北京市顺义区2022-2023学年高二下学期期末质量监测数学试题