1 . 2022年北京冬奥会开幕式中,当《雪花》这个节目开始后,一片巨大的“雪花”呈现在舞台中央,十分壮观.理论上,一片雪花的周长可以无限长,围成雪花的曲线称作“雪花曲线”,又称“科赫曲线”,是瑞典数学家科赫在1904年研究的一种分形曲线.如图是“雪花曲线”的一种形成过程:从一个正三角形开始,把每条边分成三等份,然后以各边的中间一段为底边分别向外作正三角形,再去掉底边,重复进行这一过程
![](https://img.xkw.com/dksih/QBM/2022/3/15/2937007684354048/2937566890295296/STEM/ccc416728dd940c5a95edc5670217bd6.png?resizew=484)
若第1个图中的三角形的周长为1,则第n个图形的周长为___________ ;若第1个图中的三角形的面积为1,则第n个图形的面积为___________ .
![](https://img.xkw.com/dksih/QBM/2022/3/15/2937007684354048/2937566890295296/STEM/ccc416728dd940c5a95edc5670217bd6.png?resizew=484)
若第1个图中的三角形的周长为1,则第n个图形的周长为
您最近一年使用:0次
2022-03-16更新
|
3641次组卷
|
16卷引用:重庆市第八中学校2023-2024学年高二下学期入学适应性训练数学试题
重庆市第八中学校2023-2024学年高二下学期入学适应性训练数学试题湖北省八市2022届高三下学期3月联考数学试题江苏省镇江市扬中市第二高级中学2021-2022学年高二下学期3月阶段测试数学试题浙江省杭州学军中学西溪校区2021-2022学年高二下学期4月期中数学试题(已下线)专题20 科赫曲线(已下线)考点15 数列综合问题-1-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)(已下线)高中数学 高二下-4天津市耀华中学2022-2023学年高三上学期统练(二)数学试题福建省福州第八中学2023届高三上学期质检四数学试题浙江省金华十校2022-2023学年高二上学期期末模拟数学试题辽宁省大连市庄河市高级中学2022-2023学年高二上学期12月月考数学试题山西省朔州市怀仁市2023届高三二模数学试题(已下线)专题05 数列(已下线)押新高考第16题 数列性质及其应用(已下线)专题10 数列通项公式的求法 微点2 累加法(已下线)数列的综合应用
名校
2 . 已知函数
.
(1)若
,是否存在a
,使
为偶函数,如果存在,请举例并证明,如果不存在,请说明理由;
(2)若
,判断
在
上的单调性,并用定义证明;
(3)已知
,存在
,对任意
,都有
成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e73422d2197a5a71769436381b7229.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39c1fd1da3a9e6465bb3b66894120b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5500ad00466c3f2ff8ba691f2653e6bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd456469aaa6dafb1e275183d217435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4438620ff101b83aef035104db1a6e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a1f815b0e0b6516b684a93e1850667.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e424a9e6b2505aad5eb944b00f5222bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76d0c6032c22c5d435968f414e506cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9956260c9412f340df7addda6707f3.png)
您最近一年使用:0次
2022-03-14更新
|
1233次组卷
|
3卷引用:湖南省长沙市第一中学2021-2022学年高一下学期入学考试数学试题
3 . 设集合
,其中
,
,在M的所有元素个数为K(
,2≤K≤n)的子集中,我们把每个K元子集的所有元素相加的和记为
(
,2≤K≤n),每个K元子集的最大元素之和记为
(
,2≤K≤n),每个K元子集的最小元素之和记为
(
,2≤K≤n).
(1)当n=4时,求
、
的值;
(2)当n=10时,求
的值;
(3)对任意的n≥3,
,给定的
,2≤K≤n,
是否为与n无关的定值?若是,请给出证明并求出这个定值:若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8aa469da8a950d471de1ab21529b7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5ef39c5b9867c447caba74d308f18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca2f42085784f69dce4d8df6c2751cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5ef39c5b9867c447caba74d308f18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e6b7d9861f405144acc112dbaa83719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5ef39c5b9867c447caba74d308f18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d109d041d18da77fa4bc8e8df8513d08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5ef39c5b9867c447caba74d308f18a.png)
(1)当n=4时,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57483e04fd1840c87ac5325157149877.png)
(2)当n=10时,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2114a0fe21dc0e5bf831c146ef02b113.png)
(3)对任意的n≥3,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d5ef39c5b9867c447caba74d308f18a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f7a3c9c8561ec934c904389b712fcf.png)
您最近一年使用:0次
名校
4 . 给定正整数
,定义M数列:
,
,…,
,如下:
(
,1,2,…n)等于
,
,…,
中k出现的次数.
(1)若
,M数列为:3,
,
,1,0,0,0,求
,
;
(2)证明:存在M数列,且满足
;
(3)证明:M数列是唯一的.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/831608f09609c37f757f5bfcd01253f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e93d8fb77f5bd2c0fc690752dfd771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ab1256702aef4e9f1a5eb6c12ecc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a625b91e0eba33b107550ee2a1e2f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9369d6e6f9022be0f24b7e0c7f86d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a882037b9ce104ecc496e0f31a139361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26e93d8fb77f5bd2c0fc690752dfd771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ab1256702aef4e9f1a5eb6c12ecc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a625b91e0eba33b107550ee2a1e2f4.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ab1256702aef4e9f1a5eb6c12ecc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbd67f60f04c278bdd867fdb3979dfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77ab1256702aef4e9f1a5eb6c12ecc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbd67f60f04c278bdd867fdb3979dfb.png)
(2)证明:存在M数列,且满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b6042c927a99913f5b0596f115cebb.png)
(3)证明:M数列是唯一的.
您最近一年使用:0次
名校
5 . 已知函数
,
.
(1)当
时,求
的单调区间;
(2)设函数
,
①若
有且只有一个零点,求实数a的取值范围;
②记函数
,若关于x的方程
有4个根,从小到大依次为
,
,
,
,求证:
;
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6124c9a86e0d272e2787b6d042966a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4f133cb14a3a1f0266da8cb55025ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c49bb0158e88c77d6dd95f889554eda.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5e7bc77ec1a98af267cd4763e6dc53.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
②记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cfdd1ca0b5f743ec1ac8f52414347a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b306c7aad39c01889a82f73c4d46a77.png)
![](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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/365b38a7689a8eede6820cd6f1fe952b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966729d1d3a982c6351bf63453dd55c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc37487bad04e5ab8056a6be472b2bf.png)
您最近一年使用:0次
2022-02-27更新
|
977次组卷
|
2卷引用:浙江省名校协作体2022届高三下学期开学考数学试题
名校
解题方法
6 . 三棱锥
各顶点均在表面积为
的球体表面上,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a3983cf4ab1812c6f05d80fa29ab18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de21fc87633542aee302c7b0fbfdc667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef35540101a8d7331dfe62fd1ab4d674.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.线段![]() ![]() |
D.三棱锥![]() ![]() |
您最近一年使用:0次
2022-02-25更新
|
2457次组卷
|
5卷引用:湖北省温德克英联盟2023-2024学年高二8月开学综合性难度选拔考试数学试题
湖北省温德克英联盟2023-2024学年高二8月开学综合性难度选拔考试数学试题湖北省武汉市2022届高三下学期二月调研考试数学试题重庆市第八中学2022届高三下学期调研检测(四)数学试题(已下线)专题5.1 模拟卷(1)-2022年高考数学大数据精选模拟卷(新高考地区专用)湖北省十堰市郧阳中学2021-2022学年高三2月第二次联考数学试题
名校
解题方法
7 . 已知不共线的平面向量
,
,
满足
,
,
,且
.则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560ee2894ba8c5cee6633430cc8b3b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f1a8e551cba7ec9f451749f60e628d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4e763ab6dc103b62a4f85d26b26d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559e118072fc6b4d979cef47e5020644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7565847b28502d22f899bcaf75a37b90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a3acd85bb13eacddaef154dfca05c11.png)
A.![]() ![]() ![]() |
B.![]() ![]() ![]() |
C.![]() ![]() |
D.对给定的![]() ![]() ![]() ![]() |
您最近一年使用:0次
21-22高一·湖南·课后作业
8 . 查找并阅读关于蜂房结构的资料,建立数学模型说明蜂房正面采用正六边形面,底端是封闭的六角棱锥体的底,由三个相同的菱形组成(菱形的锐角为
,钝角为
)的原因.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7192acc5f8fbc96ffeebac6a7889c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cadf7305c76ce730784b007d868d1f7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/189df1ea-86a4-4932-aa52-6e480fa888fa.png?resizew=347)
您最近一年使用:0次
9 . 已知函数
(e为自然对数的底数).
(1)求证:
时,
;
(2)设
的解为
(
,2,…),
.
①当
时,求
的取值范围;
②判断是否存在
,使得
成立,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2abd52a21627a3233cd377aa1a257189.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a90f71a22daa4df7bd75c1e3e66fcb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8a82d291105594bb2f97fb81b165d0.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2e727ac09acdaafb6c97e4f5c50aa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803092f422dcd99c23e821770b923188.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2daf2bf93c9c6fceee6b8068ee19d111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9727721cbac7d8d47c511fe934f9215d.png)
②判断是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2498a2158280a2502d58ccfc84e5bc69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2bed16e997a85f5d6d1a4d2d89a83f.png)
您最近一年使用:0次
名校
解题方法
10 . 把抛物线
沿
轴向下平移得到抛物线
.
(1)当
时,过抛物线
上一点
作切线,交抛物线
于
,
两点,求证:
;
(2)抛物线
上任意一点
向抛物线
作两条切线,从左至右切点分别为
,
.直线
交
从左至右分别为
,
两点.试判断
与
的大小关系,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471ebe959b8ff2bbabce1f0f09a36e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27fe004046f183e83376ce219c9d1bb0.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194b8ab194c7d299d5c3e0f09ec18384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2007972af3341f27fbc32ce62dfce5e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/1f30acc34f4ee1077532ae6808af2ab2.png)
(2)抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22962a2ad892cb6b14ab039a06e8cdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79cc25bc9e9c48fd18a60b95b64bb499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920ff4e858ac0ed5e5706bb77bfd5c9e.png)
您最近一年使用:0次