1 . 给定正整数m,t(
),若数列A:
满足:
,
,
,则称数列A具有性质
.
对于两个数列B:
;C:
,
定义数列
;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1666128b812bc56253aee5932dada0.png)
(1)设数列A具有性质
,数列
的通项公式为
(
),求数列
的前四项和;
(2)设数列
(
)具有性质
,数列B满足
,
,
,
且
(
).若存在一组数列
,使得
为常数列,求出m所有可能的值;
(3)设数列
(
)具有性质
(常数
),数列B满足
且
(
).若存在一组数列
,使得
为常数列,求k的最小值.(只需写出结论)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e731fd8ce3511a486bbe95e7199450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da18ad56af5e38b1a5b73f44ba198fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a406d53fd6ffd9ee6cd914f5e2b0a9bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2e48e217357ba34d190e07a6149e85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20cb8986f17cfca98e7faa063abc09f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef30011e8c2425db431204436e16629.png)
对于两个数列B:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a974a6a4d453dbb22a7b599e36f451d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae1beb8a070d3672795b2cf64ec1da6.png)
定义数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d805b6e79f2bd12ea9deda3e14261a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1666128b812bc56253aee5932dada0.png)
(1)设数列A具有性质
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708011e87fae90efc444a7477512aac0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a8100f98999e472945ab7050af50d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce69cd33d105ce280170f0cd0513026.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00725492cf521a4277f03c364998a4cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17c7608edaf9a0fa498674d5c729ae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e96fafcc7b7f783d436f853449208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fcabace2d41a5fb549da9d88c3ad33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4cf909f2febeea7d169459d0cf0bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99fe300fb6c2065f7a3783d24d9c0010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1109ca176d2be47347f68a3de238abd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9d48660f696fc51b97c89fa55d6f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed97ab77f50ae6311b37a0678ead43d5.png)
(3)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e819b87f90651d89fcd258c276294e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00725492cf521a4277f03c364998a4cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7ee076644544f8a5f9ad2ae537ba7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d438267fddcd02afff8e73c6c3fec8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4502c640ee65eb3f11364fb461c69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef78e554041f64aecdc9ca4e037b58c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1109ca176d2be47347f68a3de238abd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9d48660f696fc51b97c89fa55d6f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed97ab77f50ae6311b37a0678ead43d5.png)
您最近一年使用:0次
名校
解题方法
2 . 若函数
的定义域为
,集合
,若存在非零实数
使得任意
都有
,且
,则称
为
上的
-增长函数.
(1)已知函数
,函数
,判断
和
是否为区间
上的
增长函数,并说明理由;
(2)已知函数
,且
是区间
上的
-增长函数,求正整数
的最小值;
(3)如果
是定义域为
的奇函数,当
时,
,且
为
上的
增长函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfe5fa85f3ebdfca5b2c131582e54bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137e19310362e379bd5943525b715aaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fa744c6019195b4edcd21bde5784ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/253893d2bf2b944a6de271463c3e7929.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5222db87c8bf85e4548488f09e2d9dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a50188f84f379b3d0418c54cbade7d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f6a0eff55217e08cd9c7268ef3eecb.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a1551eabdbfb3d6f089b24fa651bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d94112851ce0deb4761bf00fcf275ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33653e42ded81460f3ae0777a786dcfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92b46d50ecc7ea20c610d9b1217582e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2021-01-15更新
|
790次组卷
|
4卷引用:上海市杨浦区控江中学2020-2021学年高一上学期期末数学试题
上海市杨浦区控江中学2020-2021学年高一上学期期末数学试题四川省雅安市2021-2022学年高一上学期期末数学试题福建省厦门双十中学2022-2023常年高一上学期期中考试数学试题(已下线)第3章 函数概念与性质(基础、典型、新文化、易错、压轴)专项训练-2022-2023学年高一数学考试满分全攻略(人教A版2019必修第一册)
名校
解题方法
3 . 王先生因病到医院求医,医生给开了个处方药(片剂),要求每天早晚8时各服一片,已知该药片每片
毫克,每
小时从体内排出这种药的
,并且如果这种药在体内的残留量超过
毫克时,就将产生副作用,请问:
(1)王先生第一天上午8时第一次服药,则第二天早晨8时服完药时,药在他体内的残留量是多少?
(2)如果王先生坚持长期服用此药,会不会产生副作用,为什么?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc011a0862d1f780331f1e9f8a467a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da45c443af7994a26ffa9d8894e7262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beddb9806191a43e6c6b194300981f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db1694dba9ccded41faa4e2110a77f45.png)
(1)王先生第一天上午8时第一次服药,则第二天早晨8时服完药时,药在他体内的残留量是多少?
(2)如果王先生坚持长期服用此药,会不会产生副作用,为什么?
您最近一年使用:0次
2021-01-01更新
|
199次组卷
|
2卷引用:上海市虹口区上海外国语大学附属外国语学校2019-2020学年高二上学期期末数学试题
名校
解题方法
4 . 对于数集X={-1,x1,x2,
,xn},其中
,n ≥ 2,定义向量集
,若对任意
,存在
,使得
,则称X具有性质P.例如{-1,1,2}具有性质P.
(1)若x > 2,且{-1,1,2,x}具有性质P,求x的值;
(2〉若X具有性质P,求证:1 ∈X ,且当xn >1 时,x1= 1;
(3)若X具有性质P,且x1= 1 ,x2 =q (q为常数),求有穷数列x1,x2,
,xn的通项公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0040b12a13d03d5f1c6c1f80ac0365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac4d197ead9c1bc27b05aedac23ad79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c122d308af408739c2717376e932122d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c6bb4424eb1e5ab02b8ac83fd6ad10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8de3dabcc3150fd539ac97718ba10c5.png)
(1)若x > 2,且{-1,1,2,x}具有性质P,求x的值;
(2〉若X具有性质P,求证:1 ∈X ,且当xn >1 时,x1= 1;
(3)若X具有性质P,且x1= 1 ,x2 =q (q为常数),求有穷数列x1,x2,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
您最近一年使用:0次
2021-08-29更新
|
542次组卷
|
6卷引用:上海市实验学校2022-2023学年高一下学期期末数学试题
名校
5 . 在△ABC中,内角A,B,C所对的边分别为a,b,c.已知a=2,c=3,又知bsinA=acos(B
).
(Ⅰ)求角B的大小、b边的长:
(Ⅱ)求sin(2A﹣B)的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d149d6494edb039646fb153d6cb00bf.png)
(Ⅰ)求角B的大小、b边的长:
(Ⅱ)求sin(2A﹣B)的值.
您最近一年使用:0次
2020-03-08更新
|
328次组卷
|
3卷引用:天津市西青区2019-2020学年高三第一学期期末考试数学试题
19-20高二·浙江·期末
名校
解题方法
6 . 直线l经过两条直线
和
的交点,且与直线
平行.
(1)求直线l的方程;
(2)求直线l与坐标轴围成的三角形面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf4f7744e04704e5363bd5d068635480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f63080caf557613ca126503b920c8ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0947dc8f5ba116aaf3239d66adc7474.png)
(1)求直线l的方程;
(2)求直线l与坐标轴围成的三角形面积.
您最近一年使用:0次
2020-03-05更新
|
118次组卷
|
4卷引用:【新东方】新东方高二数学试卷301
名校
7 . 已知函数
.
(1)若不等式
的解集是
,求a的值;
(2)当
时,求不等式
的解集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2231cd9d08a018f0953fa64f57fe8f5d.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf9ac2e604b78daca4b5f943c3335c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e95a137ad7033379aa26901fb29f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
您最近一年使用:0次
2020-03-05更新
|
587次组卷
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6卷引用:吉林省梅河口市第五中学2019-2020学年高二上学期期末数学(文)试题
名校
8 . 设
,
:函数
的定义域为R,q:函数
在区间
上有零点.
(1)若q是真命题,求a的取值范围;
(2)若
是真命题,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51d447bc3d2a0fd961b8b203c5c8b269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ba48ebe72b3a2757cd7f63eb40b795.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fab11f38ab8593932082ec4d9c8c91f.png)
(1)若q是真命题,求a的取值范围;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd81dfe9e69cb19a3b51f2a945b8ff6.png)
您最近一年使用:0次
2020-03-05更新
|
496次组卷
|
9卷引用:吉林省梅河口市第五中学2019-2020学年高二上学期期末数学(文)试题
吉林省梅河口市第五中学2019-2020学年高二上学期期末数学(文)试题吉林省梅河口市第五中学2019-2020学年高二上学期期末数学(理)试题陕西省商洛市2019-2020学年高二上学期期末数学(文)试题陕西省商洛市2019-2020学年高二上学期期末数学(理)试题河南省信阳市罗山县2020-2021学年高三第一次调研(8月联考)数学(文)试题江西省南昌市南昌县莲塘第一中学2019-2020学年高二下学期4月线上测试数学(理)试题河南省南阳市六校2020-2021学年上学期第二次联考高二年级数学试题河南省濮阳市南乐县第一高级中学2022-2023学年高三上学期9月月考文科数学试题南阳六校2022-2023学年高二上学期第二次联考数学试题
名校
解题方法
9 . 如图,在三棱台
中,
,G,H分别为
,
上的点,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/b19b21cc-55f5-42f7-bf40-abda2f68c6dd.png?resizew=156)
(1)证明:平面
平面
;
(2)若
,
,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee170c82e3dc624dc3016443496a469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac2fa4dca5cfd340a1f94c372158647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cda3d82614321b58cde7bbde4ad13eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/b19b21cc-55f5-42f7-bf40-abda2f68c6dd.png?resizew=156)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d052663101ca930843abd98cbd61c19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b6917095bea8efd3154b72d737f013.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f76925ed99b7172956319974258a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/430e2c266987203c2982b09f0ae70551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd29cc627d76412c236aac6b29fa0fdf.png)
您最近一年使用:0次
2020-03-04更新
|
740次组卷
|
6卷引用:2020届山东省青岛市胶州市高三上学期期末考试数学试题
名校
解题方法
10 . 如图,长方形
中,
,点
分别在线段
(含端点)上,
为
中点,
,设
.
![](https://img.xkw.com/dksih/QBM/2020/3/4/2412228415963136/2412349166813184/STEM/1712f70228134ab8ac2f1a738cdb8f9d.png?resizew=124)
(1)求角
的取值范围;
(2)求出
周长
关于角
的函数解析式
,并求
周长
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13fd1183dfaeedf6b71d0fb186b337c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa623f46cef6c62c8955ec7387891078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e458dd1ce1c8dcdc2becac146d9dc231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575025a5b31355d27edaffa3df1fc310.png)
![](https://img.xkw.com/dksih/QBM/2020/3/4/2412228415963136/2412349166813184/STEM/1712f70228134ab8ac2f1a738cdb8f9d.png?resizew=124)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)求出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9756177ef0c7c685e0fc62077a1cd4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd288d4152caf5fc8187a1a901c8949f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9756177ef0c7c685e0fc62077a1cd4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-03-04更新
|
586次组卷
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5卷引用:山东省青岛市胶州市2019-2020学年高一上学期期末数学试题