解题方法
1 . 已知函数
,a∈R.
(1)求
的单调区间;
(2)若对任意
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf316d7b9027a4b6827dd92615db727f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3380d40bd13f3422c1b4dabf3fd65f1c.png)
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2 . 对于实数数列{an},记
.
(1)若m1=1,m2=2,m3=4,m4=8,写出a1,a2,a3,a4的值;
(2)若数列{an}是等差数列,求证:对任意三元数组(i,j,k)(i,j,k两两不相等),总有(i﹣j)mk+(j﹣k)mi+(k﹣i)mj=0;
(3)若对任意三元数组(i,j,k)(i,j,k两两不相等),存在常数c,使得(i﹣j)mk+(j﹣k)mi+(k﹣i)mj=c,求证:{an}是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a60c8c44a5521e7ef60131c4c3808091.png)
(1)若m1=1,m2=2,m3=4,m4=8,写出a1,a2,a3,a4的值;
(2)若数列{an}是等差数列,求证:对任意三元数组(i,j,k)(i,j,k两两不相等),总有(i﹣j)mk+(j﹣k)mi+(k﹣i)mj=0;
(3)若对任意三元数组(i,j,k)(i,j,k两两不相等),存在常数c,使得(i﹣j)mk+(j﹣k)mi+(k﹣i)mj=c,求证:{an}是等差数列.
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2020-12-21更新
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262次组卷
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3卷引用:北京市密云区2021届高三上学期期中数学试题
名校
3 . 已知集合
.给出如下四个结论:
①
,且
;
②如果
,那么
;
③如果
,那么对于
,则有
;
④如果
,
,那么
.
其中,正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b7713b7f28736f2c6b9d0b9a114f62.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54e13bbde03ffad05ecc3fee8120b6a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf752ccb909d210e2a97c11880519c03.png)
②如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6a360a49f52c05c98a91334fb7bd22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf22d7d1a965bda25168a233fb6290c.png)
③如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7208b1b4a94a13f7eab532d2f17ea5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f61b6ffd8a5f51ba281f9579921496af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac385ec112e6d61b90d953e3f106ee85.png)
④如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907a89adefe08c0527238d0476727b5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7a302991409c556a2badff0d01f6c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49bf6cad08c35ca6db0e63c2d4e82497.png)
其中,正确结论的序号是
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2020-06-03更新
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1466次组卷
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5卷引用:2020届北京市密云区高三第二学期第二次阶段性测试数学试题
2020届北京市密云区高三第二学期第二次阶段性测试数学试题(已下线)第02讲 集合间的基本关系(教师版)-【帮课堂】2021-2022学年高一数学学同步精品讲义(人教A2019必修第一册)(已下线)1.2集合间的基本关系C卷河北省唐山市第一中学2021-2022学年高一上学期10月月考数学试题(已下线)高一上学期第一次月考填空题压轴题50题专练-举一反三系列
4 . 已知函数
,
.
(1)求曲线
在点
处的切线方程;
(2)求函数
的单调区间;
(3)判断函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d548b8058155d9fff8ac94cda19994a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0825c5b24d09129bb2602dd4df60d9a.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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5 . 设等差数列
的首项为0,公差为a,
;等差数列
的首项为0,公差为b,
.由数列
和
构造数表M,与数表
;
记数表M中位于第i行第j列的元素为
,其中
,(i,j=1,2,3,…).
记数表
中位于第i行第j列的元素为
,其中
(
,
,
).如:
,
.
(1)设
,
,请计算
,
,
;
(2)设
,
,试求
,
的表达式(用i,j表示),并证明:对于整数t,若t不属于数表M,则t属于数表
;
(3)设
,
,对于整数t,t不属于数表M,求t的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f0d538cab3daae7d590482989f2a35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254fa569dc952c0b78fed34c8a1daf97.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/3bac0147b641a350b592ae6a8b565a8d.png)
记数表M中位于第i行第j列的元素为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e69701dd0e5844cd75752cd391deef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49128aead2182911b2d154bf8bcd1cf2.png)
记数表
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bac0147b641a350b592ae6a8b565a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbc4957c304de68d181441625394edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0227d02cc5bfa2845d30512262a47ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2d219599bb6453e9b8b431a948ecf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7965f5d265d8b1a5bea91a427dd3a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3aabd97c086e3e1a7fcf4a419d0adf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef914cefc04d21daa7a7ec165f1d269b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c251824d22684ccb464a910c27f2e204.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab839d8569171afab5ed55c22013aa72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86718fa3bd81961f00798692fbf86db1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e05b891c5f036025713d20bf44c20704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c75905e8c61af58a59edd945b054da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ecbb868da9359eec873a17e530b634f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ce80e91fdf435a8e3ec05be990e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab1c19b66cda3fb899f06d9a25e973c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e69701dd0e5844cd75752cd391deef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cbc4957c304de68d181441625394edb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bac0147b641a350b592ae6a8b565a8d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f08ce80e91fdf435a8e3ec05be990e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab1c19b66cda3fb899f06d9a25e973c.png)
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6 . 已知函数
,若关于x的方程
有且只有两个不相等的实数根,则实数a的取值范围是_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/897d341c4021e134d49959271308088d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f965d2347c46e97c84619359fd7773a1.png)
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2020-04-28更新
|
657次组卷
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2卷引用:2020届北京市密云区高三下学期第一次阶段性测试(一模)数学试题
解题方法
7 . 已知椭圆
(
)的离心率为
, 点
在椭圆上.
(1)求椭圆
的方程;
(2)若直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
与椭圆C交于两个不同的点
,
,直线
,
与
轴分别交于
,
两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03a52d86166b0c14c76c3325d6471fd3.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11807e525dcbd910e6fb1290e26ec70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76996aac7441e306b76758d729c810a8.png)
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2020-04-08更新
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343次组卷
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2卷引用:北京市密云区2019-2020学年高二上学期期末数学试题
8 . 设数组
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238d69b84446b56240d2a8ea5de04837.png)
,数
称为数组
的元素.对于数组
,规定:
①数组
中所有元素的和为
;
②变换
,
将数组
变换成数组
,其中
表示不超过
的最大整数;
③若数组
,则当且仅当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7a172e3de92f315198a515eef6ebbe.png)
时,
.
如果对数组
中任意
个元素,存在一种分法,可将其分为两组,每组
个元素,使得两组所有元素的和相等,则称数组
具有性质
.
(Ⅰ)已知数组
,
,计算
,
,并写出数组
是否具有性质
;
(Ⅱ)已知数组
具有性质
,证明:
也具有性质
;
(Ⅲ)证明:数组
具有性质
的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad5b09d32784527e9d1201abb4ef099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238d69b84446b56240d2a8ea5de04837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c9fcb34bf3a74eae571ddad293b6cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
①数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb10fbfb7eb6d4d4ffd799cc5a363b4.png)
②变换
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916765ac224780b2ab9ad42c16b279c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
③若数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd9a9a948c76032a62a91d11fbf5bae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7a172e3de92f315198a515eef6ebbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c9fcb34bf3a74eae571ddad293b6cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7cbcf6e8ea569285cd05a6126d7190.png)
如果对数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(Ⅰ)已知数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d5994d78fc5debd0469e2a212561751.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a1a7b15221d91714fcb964379e1e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3292a7444b7e76515cee05ffe1eea50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de0f6d2b676fb885e43df4db0ed66d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(Ⅱ)已知数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b373da1d03d8fe9f96f75a1d310a24d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(Ⅲ)证明:数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50513a655f357615a650b63daf00be2c.png)
您最近一年使用:0次
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9 . 对于正整数集合
,如果任意去掉其中一个元素
之后,剩余的所有元素组成的集合都能分为两个交集为空集的集合,且这两个集合的所有元素之和相等,就称集合
为“可分集合”.
(1)判断集合
和
是否是“可分集合”(不必写过程);
(2)求证:五个元素的集合
一定不是“可分集合”;
(3)若集合
是“可分集合”.
①证明:
为奇数;
②求集合
中元素个数的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a570dbedf552f9d57ec0414e54f3386a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c4392f75c09edaec2e70c9eccb2b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)判断集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b07a67307d5d4627efa688b30e5573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38aa0ba6ea6e8f10a2159defda4e67f8.png)
(2)求证:五个元素的集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1752a1d13ec6a233405fce4d5af61d8f.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a570dbedf552f9d57ec0414e54f3386a.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
②求集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
2019-12-27更新
|
574次组卷
|
4卷引用:北京市密云区2019-2020学年高一上学期期末数学试题
北京市密云区2019-2020学年高一上学期期末数学试题北京市顺义区牛栏山第一中学2019-2020学年高三上学期期中数学试题(已下线)第1章《集合》 培优测试卷(二)-2021-2022学年高一数学上册同步培优训练系列(苏教版2019)(已下线)专题05 集合与常用逻辑用语压轴题型汇总-2021-2022学年高一《新题速递·数学》(人教A版2019)
名校
解题方法
10 . 给定整数
(
),设集合
,记集合
.
(1)若
,求集合
;
(2)若
构成以
为首项,
(
)为公差的等差数列,求证:集合
中的元素个数为
;
(3)若
构成以
为首项,
为公比的等比数列,求集合
中元素的个数及所有元素之和.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5818ede14d21f6df9ef9c2bfe09286c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e53e63811f83121eba1ca9efb17515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54d41b965c7b1771c84fabb87ae6258.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f77cadcea108fc0b1f680a8840a274c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ce64685821c3e55c07f151996ca8c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627a57cd9fdb1f586f35d9825b6bcc0b.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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2019-02-01更新
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6卷引用:上海市黄浦区2019届高三第一学期(1月)期末调研测试数学试题
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