解题方法
1 . 对于数列
,若存在
,使得对任意
,总有
,则称
为“有界变差数列”.
(1)若各项均为正数的等比数列
为有界变差数列,求其公比q的取值范围;
(2)若数列
满足
,且
,证明:
是有界变差数列;
(3)若
,
均为有界变差数列,且
,证明:
是有界变差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b12bed9580c9e3efaaae3f234780cef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)若各项均为正数的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b22febb1e578366695d7628740370bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1165edc23b5782b5942ef7e79130bb94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7c13436fc942bddb9c562520fb855a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc883e0a2ee951e94f305c807e66010a.png)
您最近一年使用:0次
2 . 已知椭圆
的长轴为4,直线
与圆
相切于点
,与
相交于
,
两点,且
,
,
.
(1)记
的离心率为
,证明:
;
(2)若
轴右侧的点
在
上,且
轴,
,
是圆
的两条切线,切点分别为
,
(
在
上方),求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4966973694e3fdf6b63434b7bee5911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbd6303756adb878c1e028f511e51f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b32a5bdae1e1c0082553d71b80dbcd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6270bb08b90f72d5671ab8225f356c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f99df1a7b58018125b99578b779342.png)
(1)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3a16563ac359fda8ac16989aa704b23.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af72fe2d8fdcd6793597db51d070290e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8305c4ffbf876642440c3d28e91e9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce2790947716b1cfa9c5e7a65db4093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45b79e16fb149b3ea933cd087f0cc740.png)
您最近一年使用:0次
名校
3 . 多元导数在微积分学中有重要的应用.设
是由
,
,
…等多个自变量唯一确定的因变量,则当
变化为
时,
变化为
,记
为
对
的导数,其符号为
.和一般导数一样,若在
上,已知
,则
随着
的增大而增大;反之,已知
,则
随着
的增大而减小.多元导数除满足一般分式的运算性质外,还具有下列性质:①可加性:
;②乘法法则:
;③除法法则:
;④复合法则:
.记
.(
为自然对数的底数),
(1)写出
和
的表达式;
(2)已知方程
有两实根
,
.
①求出
的取值范围;
②证明
,并写出
随
的变化趋势.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9265c54f2a96bf290388484cfd0ff47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7c75f7dcce2b59c10237868c6715ffb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c137b971df3492a2001085d98706801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1343590f4aaf6b9e3f3c200e318bfea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43887f94250f6c073e144f2ae39b3021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8baf79cfbc5cc29029ca66632c20775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcf1c89ff75dc38ce474a01c4932f8c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff01089fbfd66ae3411b15e54f7a9120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef134baac9bb96324f585c5e532cbefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09df69561e70f6d8a66d32f7ffa8a60d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/272a7f552e7d99ab3756c1d4e64fc355.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9e8e03d12633cfe6858b8c85047100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d6ee0cf2632c76087f5bce01358ef8.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b0e3a7c0dc3c1143610f60a0fd884f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1343590f4aaf6b9e3f3c200e318bfea0.png)
(2)已知方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
①求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
②证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18df306af443a02bf538cfc517d4a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450398974b1561ca801e102e16df6789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-02-21更新
|
1077次组卷
|
3卷引用:广东省广州市华南师范大学附属中学2024届高三上学期数学周测试题(12)
广东省广州市华南师范大学附属中学2024届高三上学期数学周测试题(12)(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编江苏省海安高级中学2023-2024学年高二下学期第二次月考数学试题
22-23高三下·北京海淀·开学考试
名校
解题方法
4 . 若无穷数列
的各项均为整数.且对于
,
,都存在
,使得
,则称数列
满足性质P.
(1)判断下列数列是否满足性质P,并说明理由.
①
,
,2,3,…;
②
,
,2,3,….
(2)若数列
满足性质P,且
,求证:集合
为无限集;
(3)若周期数列
满足性质P,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9672f1800f9544e878955f289aa3fc6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f2c7c9305b404f7363a376af101aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aa38a89b95fa1ea7bfc91630f6c7437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e0fbad04faddb5408ce4e7e6e3ed816.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(1)判断下列数列是否满足性质P,并说明理由.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b80c1ed7b10ac7ca1cd81cdd39a8fcc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ce6401cf48b9546342b1b96ac2cc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f224a5a66c91792eceb8f8c725183f67.png)
(3)若周期数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2024-02-10更新
|
1553次组卷
|
14卷引用:北京市海淀区清华大学附属中学2023届高三下学期开学调研测试数学试题
(已下线)北京市海淀区清华大学附属中学2023届高三下学期开学调研测试数学试题北京市第五中学2023届高三下学期3月检测数学试题北京市海淀区教师进修学校附属实验学校2023届高三零模数学试题(已下线)2023年北京高考数学真题变式题16-21北京市清华大学附属中学2023届高三下学期4月月考数学试题北京市海淀区中国人民大学附属中学2022-2023学年高二下学期期中数学复习试题(2)北京市海淀区首都师范大学附属中学2023-2024学年高三上学期阶段练习(1月)数学试题(已下线)北京市第四中学2023-2024学年高三下学期开学考试数学试题湖南省2024届高三数学新改革提高训练一(九省联考题型)2024届高三新改革数学模拟预测训练一(九省联考题型)(已下线)压轴题05数列压轴题15题型汇总-1北京市顺义区第一中学2024届高三下学期高考考前适应性检测数学试卷广东省广州市执信中学2024届高三下学期教学情况检测(二)数学试题湖南省张家界市民族中学2023-2024学年高二下学期入学考试数学试题
5 . 定义:过曲线上的某一点向曲线的凹侧作与曲线相切的圆,当该圆的半径最大时,该圆的半径称为曲线在该点处的曲率半径.则下列说法正确的有__________ .
①双曲线
在顶点处的曲率半径为
;
②曲线
在点
处的曲率半径最小;
③若椭圆
在上顶点处的曲率半径与在右顶点处的曲率半径之比为8,则该椭圆的离心率为
①双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35447d4356ff134546ddf83c9adb992e.png)
②曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05616bd6fa88a792267570ac3e7e212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
③若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
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6 . 已知函数
,点
为平面内一点,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81cbc38dede229ac885633f63550e685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/493f7a6fe5c1e676672547297082e64d.png)
A.当![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.若过点![]() ![]() ![]() ![]() |
D.若过点![]() ![]() ![]() ![]() |
您最近一年使用:0次
7 . 设
是正实数数列.
(1)若
收敛,求证:存在严格递增的无界正实数数列
满足
收敛.
(2)若
收敛,是否一定存在严格递增的正整数数列
,满足
收敛,且
?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7376941fa463c63b1d4d4ea866b78c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccecde965d7557d5ee35dea8ae7164a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60c988a3683540149b687486af0ed3a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120dcd9c3adc5b08ab9d84f228cc4b90.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ad99ac2f9cbe69281dcdc7d4195d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba58d775c69de6d132c58581d614792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246e5563a2f86de45879b21393d814f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c69eef9b8e90f6a153b87738f759bcf.png)
您最近一年使用:0次
8 . 设
,满足
.
(1)证明:若
,则当
时,
.
(2)若存在
满足
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e761714f6940c2c06c5750e2ed80cc4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fbd27b6b4143c730ab9d36393a5fe14.png)
(1)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c61cfbfd3bf888856b7dc9b2a84c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac247d375e0da7fddafad1aa8186aa51.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4439c7de7291f79def06d548603de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa3205b1df826d63914dcb55bb3ab43.png)
您最近一年使用:0次
9 . 设
为全体由
和1构成的
元数组的集合,其中
为偶数.称
与
正交,若
.记
为可以从
中选出
元数组个数的最大值,满足选出的数组两两正交.求
和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318f55d136f3b38a2a5f529fd17f1f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91b4cd18676efcd11a591ab3e4d2085b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea378cc281cb24fc593bedb34dab3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4fc8faefb26b233d4aa9dbef043aae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc3f52cd9edf88e49e2409f050108d.png)
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10 . 若函数
在
上单调递增,则a和b的可能取值为( )
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A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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2024-01-25更新
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904次组卷
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5卷引用:湖南省衡阳市第八中学2024届高三上学期第一次模拟测试数学试题