名校
解题方法
1 . 如图,在平面四边形
中,
,
.若
,则四边形
的面积为______ ;若
的大小可变化,则
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8ebac9bde6bb6a2113edb90bf963fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8eab10e24f9b016f46995a895237929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2947ca8e0cdbeb4aab80ce9e7b63ba98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
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2 . 已知函数
.
(1)试讨论函数
的单调性;
(2)当
时,不等式
恒成立,求整数
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ae10144aef6e54cab4e8b4582f04b8.png)
(1)试讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5184782e1e51cebf8996770dcd62d7fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-05-08更新
|
575次组卷
|
2卷引用:吉林省长春市第五中学2023-2024学年高二下学期第一学程考试数学试题
3 . “0,1数列”在通信技术中有着重要应用,它是指各项的值都等于0或1的数列.设
是一个有限“0,1数列”,
表示把
中每个0都变为
,每个1都变为
,所得到的新的“0,1数列”.例如
,则
.设
是一个有限“0,1数列”,定义
.若有限“0,1数列”
,则数列
的所有项之和为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38e3d87be9f706832ef25537d78a201b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823b15e6dc9fce202c3c57e7d18df0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f32df58be46198b2e7a112ed255d8bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e502eff0c1fe80b2a546ea4af17a9755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde81bb00224b2a80ba56c6ce27b94a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36091df0a9c71ef14161ba59dbaa4230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374de27c75bc2269806d5b44d1518c82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e645ae0b78ad4ca300e3889ca3f9bcce.png)
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4 . 已知函数
在点
处的切线方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88a6a43f7d0342e741608047f533386.png)
(1)求
;
(2)求
的单调区间;
(3)求使
成立的最小整数
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54c354a9dbdd1540ca6911dde07fc530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88a6a43f7d0342e741608047f533386.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)求使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f3e3aa6cd1c5d74a542d3d17950c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
5 . 设
是自然对数的底数,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d678337d7747aa35cf6ad8aa98907ba.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
6 . 如图,正方形ABCD的边长为1,P,Q分别为边BC,CD上的点,且
;
(2)求
面积的最小值;
(3)某同学在探求过程中发现PQ的长也有最小值,结合(2)他猜想“
中PQ边上的高为定值”,他的猜想对吗?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e50966267b44a653055ab15c490536.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
(3)某同学在探求过程中发现PQ的长也有最小值,结合(2)他猜想“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
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2024-04-20更新
|
534次组卷
|
2卷引用:吉林省长春市第二实验中学2023-2024学年高一下学期4月月考数学试题
名校
7 . 给出定义:对于向量
,若函数
,则称向量
为函数
的伴随向量,同时称函数
为向量
的伴随函数.
(1)设向量
的伴随函数为
,若
,且
,求
的值;
(2)已知
,
,函数
的伴随向量为
,请问函数
的图象上是否存在一点
,使得
,若存在,求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c85e3f270228f575ce19d616ccc6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce34827ae0930934dc5a6f1d52acd5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
(1)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136d9091bebc9137052a129f6b2ce0a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b29cbe1cd5532afd6ae70d27be77bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca7583f1a94fb9e8101fbdb0570260d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad963e4119950b4762f513012b273a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df46b800478f98f9f7b4f4c51a90a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd3439b741456cee344e7f9cbf2cc293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4cde2cd329c08d92abda7098137d1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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8 . 已知函数
,则下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/250954bba2b5f0b7e33208a19147e2d3.png)
A.当![]() ![]() |
B.存在定直线始终与曲线相切 |
C.存在实数![]() ![]() |
D.存在实数![]() ![]() |
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9 . 若实数
,
分别是方程
,
的根,则
的值为______ .
![](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/22c8cd775fba88d87428dab41260b308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b953e06f7a01faeace7176ddd2d77c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3049273653a7a4d7f6252d0c1f05164.png)
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2024-04-15更新
|
465次组卷
|
2卷引用:吉林省长春市第二中学2023-2024学年高二下学期第一学程考试(4月)数学试题
10 . 已知
是数列
的前
项和,且
,
(
),则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8323901a49cac29afd7d62864f088077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac93306dbacb99db7b341874bb3413a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
A.数列![]() | B.数列![]() |
C.![]() | D.![]() |
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