1 . 若某类数列
满足“
,且
”
,则称这个数列
为“
型数列”.
(1)若数列
满足
,求
的值并证明:数列
是“
型数列”;
(2)若数列
的各项均为正整数,且
为“
型数列”,记
,数列
为等比数列,公比
为正整数,当
不是“
型数列”时,
(i)求数列
的通项公式;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b781279c765cfbfb88b28bc5b6cfb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa01f03fb074bff35b35e07047d11b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be613fff0421d9be9e8bb5eb8b07c40f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00cf22c8daa450289ffdce46b85024b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe61d313eeca8ba47478a9de40540db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85726f99979d3793ea28b77a7708f4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07cefac60bb3fcde0bded804501c90b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(i)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c15b6cf3d2cdd85baed3056ac375d3c.png)
您最近一年使用:0次
名校
解题方法
2 . 已知椭圆
过点
,焦距是短半轴长的
倍,
(1)求椭圆
的方程;
(2)点
是椭圆
上的三个不同点,线段
交
轴于点
异于坐标原点
,且总有
的面积与
的面积相等,直线
分别交
轴于点
两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81687c0af83f550bcb802e2d82c76a61.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88241f8018e6693c7047bf6442f83390.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3904463e169fb25dbd36fa257edd2bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d42ca9316de7be10d095b5b9dc9748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f02ed682ee981bfa4aeb2de96771be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43995a8753fb39e768bc0e04a0e2a7b3.png)
您最近一年使用:0次
2024-03-29更新
|
1094次组卷
|
3卷引用:数学(天津卷03)
2024高三下·天津·专题练习
解题方法
3 . 已知函数
.
(1)当
时,求
在点
处的切线方程;
(2)若对
,都有
恒成立,求
的取值范围;
(3)已知
,若
,
且满足
,使得
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b572d532418dd2e65b58235cefb449c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bea9227dd0104da58e0c40952cc87ed.png)
(2)若对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/191e3c845e90f229f3c992aff85b92db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d5293e346763d59b4e64ae0fd8f675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86363d44047e7a13439be95c5ada424f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d41acc47493556617fe7b9e55093d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2037b0bad7c7a312bac1ac0653d9a491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500cc91e21777edad7e5a84668378daa.png)
您最近一年使用:0次
解题方法
4 . 甲、乙、丙、丁四位同学参加跳台滑雪、越野滑雪、单板滑雪三个项目的比赛,每人只能参加一个项目,每个项目至少一个人参加,且甲、乙两人不能参加同一项目的比赛,则四人参加比赛的不同方案一共有_____ 种;如果符合以上条件的各种方案出现的概率相等,定义事件A为丙和丁参加的项目不同,事件B为甲和乙恰好有一人参加跳台滑雪,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed6ed1283718f746105c18bd8b72c3b.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed6ed1283718f746105c18bd8b72c3b.png)
您最近一年使用:0次
2024-03-06更新
|
2022次组卷
|
5卷引用:2024年天津高考数学真题平行卷(提升)
(已下线)2024年天津高考数学真题平行卷(提升)(已下线)第七章 概率初步(续)(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)辽宁省名校联盟2023-2024学年高二下学期3月联合考试数学试卷(已下线)高二下学期期中复习填空题压轴题十五大题型专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)广西五校2023-2024学年高二下学期5月联考数学试题
名校
解题方法
5 . 任取一个正整数,若是奇数,就将该数乘3再加上1;若是偶数,就将该数除以2.反复进行上述两种运算,经过有限次步骤后,必进入循环圈
.这就是数学史上著名的“冰雹猜想”(又称“角谷猜想”).如取正整数
,根据上述运算法则得出
,共需经过8个步骤变成1(简称为8步“雹程”).现给出冰雹猜想的递推关系如下:已知数列
满足:
(
为正整数),
当
时,
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a16f78ce0dab1ac8fa6abbd70f2b008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3967d620e2fef3ecc724c66e29f68a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73700b5135fc6a9c2d923a27a4c9b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999ac8c1ef39251e07a7fc54cbf7e26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4914df4e75585d5ff7709d64a23611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59097ad7c8f3fcff871ad48933d30498.png)
A.170 | B.168 | C.130 | D.172 |
您最近一年使用:0次
2024-01-12更新
|
921次组卷
|
4卷引用:信息必刷卷04(天津专用)
6 . 已知数列
为等差数列,数列
为等比数列,且
,
,
,
(
).
(1)求
,
的通项公式;
(2)已知
,求数列
的前
项和
;
(3)求证:
(
).
![](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/2a0d29f34218cd60cc6e9ce4dcd13925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5aa46a7512675ab55f82d18ca3cc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d1279460f2d2eca25ef419cd17ec6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f287759fad50450b0bf4f69ee80ecdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd85b79372dc6e596d465f738c3c300.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f759116865a2bacd2515981e7af2b552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232c753e94442cf89732ce7e9ac0ee1f.png)
您最近一年使用:0次
2023-11-22更新
|
1033次组卷
|
4卷引用:黄金卷05
(已下线)黄金卷05天津市滨海新区塘沽第一中学2024届高三上学期第二次月考(期中)数学试题天津市河东区第三十二中学2024届高三上学期第二次月考数学试题(已下线)专题09 数列的通项公式、数列求和及综合应用(9大核心考点)(讲义)
解题方法
7 . 已知函数
.
(1)当
时,求曲线
在点
处的切线方程;
(2)当
时,求使
恒成立的最大偶数
.
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db26990def13099db22a6630a84b71f.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5828873f8369183faf71181cda5b61d2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9807631136840cb8da536aae933cbedf.png)
您最近一年使用:0次
8 . 已知函数
,若函数
有6个零点,则
的值可能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58523796d9de0f00b3b97c6137a9c0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe96e0e991adcccb7afdb3273d7cc80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 已知
中,
,
,
,
,
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2e679d7b314ff58c284da08e8edbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fce0b59d0151d693deb69178a688ff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecda5a0d9d1ec48be73edb5ec0559785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0600e615377da8976b62331c73612327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7bc61fc10d8c36312cb86346ba8ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14329b73af66646b981e106896efdc10.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-09-29更新
|
1657次组卷
|
11卷引用:黄金卷04
(已下线)黄金卷04(已下线)第一讲:数形结合思想【练】天津市北辰区第四十七中学2024届高三上学期第二次阶段性检测数学试题(已下线)专题01 平面向量压轴题(2)-【常考压轴题】(已下线)专题5.2 平面向量的数量积及其应用【七大题型】(已下线)重难点09 平面向量常考经典压轴小题全归类【九大题型】(已下线)专题07 平面几何中的向量方法 向量在物理中的应用-《重难点题型·高分突破》(人教A版2019必修第二册)(已下线)专题06 平面向量的坐标表示(2)-《重难点题型·高分突破》(苏教版2019必修第二册)(已下线)压轴题06向量、复数压轴题16题型汇总-1(已下线)【练】 专题一 平面向量线性运算的最值问题(压轴大全)河南省开封市通许县等3地2023届高三信息押题卷理科数学试题
10 . 如图所示,在四棱锥
中,底面
为矩形,侧面
为正三角形,且
分别为
的中点,
在线段
上,且
.
平面
;
(2)当
时,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c5afecdc6f473c34262eb7f8420f8f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2829867f57687a3a35a62142aae5c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e297d1a6f7f2ed41b2d909b19b140c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c1a03f93b56a1fb0b57d20d53b4323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a83a7c9322e990dafee3e7b87ed7385.png)
您最近一年使用:0次