名校
1 . 对于定义在
上的函数
,如果存在一组常数
,
,…,
(
为正整数,且
),使得
,
,则称函数
为“
阶零和函数”.
(1)若函数
,
,请直接写出
,
是否为“2阶零和函数”;
(2)判断“
为2阶零和函数”是“
为周期函数”的什么条件(用“充分不必要条件”“必要不充分条件”“充要条件”或“既不充分也不必要”回答),并证明你的结论;
(3)判断下列函数是否为“3阶零和函数”,并说明理由.
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7f4cc0837a4e6dcd0072887e4e2704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe6d9f54a34762aadfdf8e2bac977cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892519541cfba6f2763cd29159bf1b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329fb959f16f82835aa68fca9d3f08f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcda6a21da79726f8fb3ba6235b9010f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebef85c05f6d84ceb67d92abf77ba2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ace630100e64ed290d82936ad249c8.png)
(2)判断“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)判断下列函数是否为“3阶零和函数”,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ab7da79b2400cf8125ef040cd056b76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/321b15db96dc89f136a7421e09fc9814.png)
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22-23高二下·上海·期中
2 . 已知无穷数列
(
)的前n项和为
,记
,
,…,
中奇数的个数为
.
(1)若
,请写出数列
的前5项;
(2)求证:“
为奇数,
,3,4,
为偶数”是“数列
是严格增数列的充分不必要条件;
(3)若
,
2,3,
,求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d1a511265fdde77ed111876f337458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64810519cca09d8bad1e5c0720b6f70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccae0d8c29b807d2844ba1e61633a6e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)求证:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391621c6a983318f5eb3085ede2cc8a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14be3a67d7ff26e1850b3d5f891b7e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7a172e3de92f315198a515eef6ebbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b1e185d6a0ab350cdc947beeb82040.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07096af3b99fd1cb11c31f19a2c6408e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d1a511265fdde77ed111876f337458.png)
您最近一年使用:0次
名校
3 . 已知无穷数列
满足
.
(1)若对于任意
,有
.
(ⅰ)当
时,求
,
;
(ⅱ)求证:“
”是“
,
,
,
,
为等差数列”的充分不必要条件.
(2)若
,对于任意
,有
,求证:数列
不含等于零的项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
(1)若对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5771cdf6cb1557e3772648a8bea28eb9.png)
(ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0748c346ed88f98e424de8edf278325.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
(ⅱ)求证:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/204476aac1a5c62589156d83ff19fe16.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/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce88126c3cbc88e03d38f56b7da315b6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98d94ba0c7e8fccfb517f4e1560c20a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c63b69d02b70e2e0af7c523dea95b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
2023-07-09更新
|
250次组卷
|
2卷引用:北京市顺义区2022-2023学年高二下学期期中考试数学试题
名校
解题方法
4 . 已知无穷数列
的各项均为整数.设数列
的前
项和为
,记
中奇数的个数为
.
(1)若
,试写出数列
的前5项;
(2)证明:“
为奇数,且
为偶数”是“数列
为严格增数列”的充分非必要条件;
(3)若
(
为正整数),求数列
的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41274819307283f0a931fb244401733e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a229173b0f235a4da8aeb6d35f1325f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549d08f011d91ff3f40426a1db0adf12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7a172e3de92f315198a515eef6ebbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
您最近一年使用:0次
名校
5 . (1)判断:对于三个实数a、b、c,“
”是“
或
”的 条件(填“充要”、“充分非必要”、“必要非充分”、“既非充分也非必要”),并证明.
(2)证明:
是无理数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2958030ec9d7543dda1f529593a915e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098943e98ad321740f83f0bb67004598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad5e009486af263893ca8290be72f258.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
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6 . 已知集合
.
(1)判断8、9、10是否属于集合A;
(2)已知
,证明:“
”的充分非必要条件是“
”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b528ebb0e57c521e91fa0bad429ca915.png)
(1)判断8、9、10是否属于集合A;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503a6aba878045f13cf45b1e0fc7be7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc4c15b1d62420f42732db3b626ce3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a3a95a978c23259caf993285d987b3.png)
您最近一年使用:0次
2022-10-24更新
|
989次组卷
|
8卷引用:上海市朱家角中学2022-2023学年高一上学期10月月考数学试题
上海市朱家角中学2022-2023学年高一上学期10月月考数学试题2023年3月河北省普通高中学业水平合格性考试模拟(五)数学试题河南省周口恒大中学2022-2023学年高一下学期2月月考数学试题(已下线)1.4 充分条件与必要条件(5大题型)精讲-【题型分类归纳】(已下线)2.2 充分条件、必要条件、充要条件(5大题型)-【题型分类归纳】(苏教版2019必修第一册)(已下线)1.2 常用逻辑用语-高一数学同步精品课堂(沪教版2020必修第一册)贵州省黔西南州金成实验学校2023-2024学年高一上学期第一次月考数学试题上海市曹杨第二中学2023-2024学年高一上学期第一次月考(10月)数学试题
名校
7 . 已知f(x)是定义在[0,+∞)上的函数,满足:①对任意x∈[0,+∞),均有f(x)>0;②对任意0≤x1<x2,均有f(x1)≠f(x2).数列{an}满足:a1=0,an+1=an+
,n∈N*.
(1)若函数f(x)=
(x≥0),求实数a的取值范围;
(2)若函数f(x)在[0,+∞)上单调递减,求证:对任意正实数M,均存在n0∈N*,使得n>n0时,均有an>M;
(3)求证:“函数f(x)在[0,+∞)上单调递增”是“存在n∈N*,使得f(an+1)<2f(an)”的充分非必要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e4ac5a6256d5c9976c767898d14c3a0.png)
(1)若函数f(x)=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1edaf436c76d5e11f1700fb36a2af15.png)
(2)若函数f(x)在[0,+∞)上单调递减,求证:对任意正实数M,均存在n0∈N*,使得n>n0时,均有an>M;
(3)求证:“函数f(x)在[0,+∞)上单调递增”是“存在n∈N*,使得f(an+1)<2f(an)”的充分非必要条件.
您最近一年使用:0次
2021-04-20更新
|
467次组卷
|
6卷引用:2020届上海市上海交通大学附属中学高三下学期考前测试数学试题
2020届上海市上海交通大学附属中学高三下学期考前测试数学试题(已下线)第一单元 集合与常用逻辑用语(A卷 基础过关检测)-2021年高考数学(文)一轮复习单元滚动双测卷(已下线)第1章 常用逻辑用语(基础卷)-2020-2021学年高二数学课时同步练(苏教版选修2-1)(已下线)单元卷 常用逻辑用语(基础卷)-2020-2021学年高二数学课时同步练(苏教版选修1-1)(已下线)1.2 充分条件与必要条件提高练-2021-2022学年高二数学同步训练精选新题汇编(人教A版选修2-1)(已下线)考向29 推理与证明-备战2022年高考数学一轮复习考点微专题(上海专用)
18-19高二上·广东深圳·期中
名校
8 . 定义:如果存在实数x,y使
,那么就说向量
可由向量
线性表出.给出命题:p:空间三个非零向量
中存在一个向量可由另两个向量线性表出.q:空间三个非零向量
共面.判断p是q的什么条件,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946b98d3f67e56ffc7cf6afa7b286235.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/847fb7661543522ad8935b9057a18b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003445ad39d3a481ebe44ffba3030f21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7adb3b57d3f2358cef9dbf811cb86349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7adb3b57d3f2358cef9dbf811cb86349.png)
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名校
9 . 如果实系数
、
、
和
、
、
都是非零常数.
(1)设不等式
和
的解集分别是
、
,试问
是
的什么条件?并说明理由.
(2)在实数集中,方程
和
的解集分别为
和
,试问
是
的什么条件?并说明理由.
(3)在复数集中,方程
和
的解集分别为
和
,证明:
是
的充要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7936359df4c926b72b48c6fdae55f12d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b76f79be89b8c6227b68eded6b675546.png)
(1)设不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0826c48a346e7d6eca890d10c9785ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ea3eb7bfc845b94b731bd4d5279192.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/4c71dad98ca8479b3fef6d80d05ebbe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
(2)在实数集中,方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ffc83b103ff29143b70ca14b44c37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add6d5ac2225c70d9c6103a6ee4d3f23.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/4c71dad98ca8479b3fef6d80d05ebbe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
(3)在复数集中,方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ffc83b103ff29143b70ca14b44c37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add6d5ac2225c70d9c6103a6ee4d3f23.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/4c71dad98ca8479b3fef6d80d05ebbe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a70d32c64918aa4d1d9d3ce0bdbf7b.png)
您最近一年使用:0次
2020-02-04更新
|
485次组卷
|
7卷引用:2017届上海市上海中学高考数学模拟试卷(6)数学试题
2017届上海市上海中学高考数学模拟试卷(6)数学试题(已下线)1.2.2+充要条件(重点练)-2020-2021学年高二数学(文)十分钟同步课堂专练(人教A版选修1-1)(已下线)1.2.2+充要条件(重点练)-2020-2021学年高二数学(理)十分钟同步课堂专练(人教A版选修2-1)(已下线)热点01 集合与逻辑-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)专题01 集合与常用逻辑用语-【备战高考】2021年高三数学高考复习刷题宝典(压轴题专练)(已下线)专题02 常用逻辑用语-备战2022年高考数学学霸纠错(全国通用)(已下线)高一上学期第一次月考解答题压轴题50题专练-举一反三系列
名校
10 . 已知函数
,其中
.
(1)求函数
的零点个数;
(2)证明:
是函数
存在最小值的充分而不必要条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61842bca8c7387474ed7e10d5f78878b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08290af79305df59bc0a1fc2b7c4f7c5.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3a34d6f60032718820c3da2b07786b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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2017-05-21更新
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3卷引用:北京市西城区2017届高三5月模拟测试(二模)数学理试卷
北京市西城区2017届高三5月模拟测试(二模)数学理试卷福建省厦门外国语学校2018届高三下学期第一次(开学)考试数学(理)试题(已下线)2018年高考二轮复习测试专项【苏教版】专题一 集合与简易逻辑