名校
1 . 设正整数数列
,
,
,
满足
,其中
.如果存在
,3,
,
,使得数列
中任意
项的算术平均值均为整数,则称
为“
阶平衡数列”
(1)判断数列2,4,6,8,10和数列1,5,9,13,17是否为“4阶平衡数列”?
(2)若
为偶数,证明:数列
,2,3,
,
不是“
阶平衡数列”,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246f051291c76972cc3bd4a4f82f2342.png)
(3)如果
,且对于任意
,数列
均为“
阶平衡数列”,求数列
中所有元素之和的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140b9dbcada4ac2e5fe3cc30009bcd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a682c1e08d96bf4dc8d674b4b6a1c920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/431acf301f0cf1e414b532de94708474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb62c59018da6ef27b45a210c675129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad48b0279100c0f6958fdba11d84b03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3550c48a81ab687bbcdd8fdc6931701f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)判断数列2,4,6,8,10和数列1,5,9,13,17是否为“4阶平衡数列”?
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f344a2d8d76fad8cbecaffc44f11f907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246f051291c76972cc3bd4a4f82f2342.png)
(3)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0da1b6e7328f7540c2e964874fbc4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246f051291c76972cc3bd4a4f82f2342.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2024-01-14更新
|
1110次组卷
|
9卷引用:北京西城区2019届高三上学期期末数学(理)试题
北京西城区2019届高三上学期期末数学(理)试题云南省昆明市云南师范大学实验中学2023-2024学年高二下学期3月月考数学试题(已下线)数学-2022届高三下学期开学摸底考试卷(北京专用)(已下线)北京市第四中学2022届高三下学期开学考试数学试题北京市第三中学2023届高三上学期期中学业测试数学试题北京市陈经纶中学2023届高三下学期综合练习一(开学考试)数学试题上海市吴淞中学2021-2022学年高二上学期期末数学试题(已下线)期末真题必刷压轴60题(22个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)2024年普通高等学校招生全国统一考试数学冲刺卷一(九省联考题型)
解题方法
2 . 已知中心在原点
,对称轴为坐标轴的椭圆
的其中一个焦点在抛物线
的准线上,并且椭圆
的左顶点到左焦点的距离为
.
(1)求椭圆
的标准方程;
(2)一条直线
与椭圆C分别交于A,B两点,且
,试问点O到直线AB的距离是否为定值,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349ec9acf5d370c87fc7fd5c16f057b5.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)一条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
您最近一年使用:0次
名校
3 . 已知定义在R上的偶函数
和奇函数
满足
(
且
),且
.
(1)求函数
和
的解析式;
(2)判断并证明函数
在定义域上的单调性;
(3)若函数
的最小值为
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d59564fe16ca72735148d3abcc9c174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbeaa8fac51a4c8b4420db8c91eb921.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)判断并证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e068b6c2fdc6f7e4a0573662a4d1247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a94acdfb41489d5694b5a64b9e99754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2021-04-01更新
|
1347次组卷
|
3卷引用:江苏省南通市通州高级中学2020-2021学年高一上学期期中数学试题
江苏省南通市通州高级中学2020-2021学年高一上学期期中数学试题云南省昆明市第一中学2021-2022年高一上学期期中考数学试题(已下线)第09练 指数与指数函数-2022年【寒假分层作业】高一数学(人教A版2019选择性必修第一册)
解题方法
4 . 已知
.
(1)证明:
;
(2)对任意
,
,求整数
的最大值.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6068e5fccbb144797b212bc8b9a6f7a2.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1136ca42f76bcb8ecbec5cf2c29b6121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b596e3c50904ae44375647f0f322d2b.png)
您最近一年使用:0次
名校
5 . 已知函数
,在点
处的切线为
.
(1)求
,
的值及函数
的单调区间;
(2)若
,
是函数
的两个极值点,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0c3243e8eed9b404423f81a627f85f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](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/99b5403b296ab61d53dd176e2c3e7349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13e5c66b641e6f5bfddff5d1997a34.png)
您最近一年使用:0次
2020-10-08更新
|
485次组卷
|
2卷引用:重庆市西南大学附属中学2021届高三上学期第一次月考数学试题
名校
解题方法
6 . 已知函数
,
,
,且
的最小值为0.
(1)若
的极大值为
,求
的单调减区间;
(2)若
,
的是
的两个极值点,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd125568cf7100a22c4ec73698f7474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90e8d5d7fed033f48270b1ff825fcd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8806602a7954aa6a067d8c6aed8e239f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](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/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2349e3509799b01ce88ce91a0d7dda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93c72cdf3b7f15f2b775e80ac15de403.png)
您最近一年使用:0次
2020-06-15更新
|
3800次组卷
|
4卷引用:云南省昆明市第一中学2020届高三考前第九次适应性训练数学(理)试题
云南省昆明市第一中学2020届高三考前第九次适应性训练数学(理)试题(已下线)专题21 函数与导数综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)(已下线)极值点偏移专题08极值点偏移的终极套路新疆维吾尔自治区乌鲁木齐市第四十中学2024届高三上学期11月月考数学试题
名校
解题方法
7 . 已知函数
,
.
(1)当
时,设函数
在区间
上的最小值为
,求
;
(2)设
,若函数
有两个极值点
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a35c267862c082fbdd4e6dce769de0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83eb829e3338a9e4be598124855685e8.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9210e75c35fb455d0446eb7ddba7d79c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812b1efe6b4a2c6cdabfaf0d903bfecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f252477a0de25fb08083c50b12b9fbb.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6dce404b0bd7671b522eb99ca71f76.png)
您最近一年使用:0次
2020-04-21更新
|
712次组卷
|
5卷引用:2020届百师联盟高三练习题(一)(全国卷 II)数学(理)试题
解题方法
8 . 已知椭圆
的中心为坐标原点
,焦点在
轴上,离心率为
,
分别为椭圆
的左、右焦点,点
在椭圆
上,以线段
为直径的圆经过点
,线段
与
轴交于点
,且
.
(1)求椭圆
的方程;
(2)设动直线
与椭圆
交于
两点,且
.求证:动直线
与
圆相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da01a3abe1c9dc4e6283afa0dc1a0d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f2188d99b44972f1e13d3a339ee5c7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2abe13e2d4176f55f71677bbbb6eb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2845cff59808d0945644a6c867e40740.png)
您最近一年使用:0次
9 . 已知函数
.
(1)讨论
的单调性;
(2)证明:
.注:
为自然对数的底数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068132ef9604287c220c731012efec01.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f2df1570205c3018e8562cce8a3f57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
您最近一年使用:0次
2020-05-22更新
|
560次组卷
|
3卷引用:云南省玉溪市2019-2020学年高三第二次教学质量检测数学(理)试题
云南省玉溪市2019-2020学年高三第二次教学质量检测数学(理)试题江西省赣州市十五县(市)2019-2020学年高二下学期期中联考数学(理)试题(已下线)专题21 函数与导数综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)
名校
10 . 已知函数
,且
.
(1)求
;
(2)证明:
存在唯一极大值点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427a3493f9402bd8c042b71362a0b0ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babc2bdb59e9ae1821bd48e7395474d8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03fdeabee5d81770621fddb60562e7f7.png)
您最近一年使用:0次