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1 . 阿基米德螺线广泛存在于自然界中,具有重要作用.如图,在平面直角坐标系xOy中,螺线与坐标轴依次交于点
,
,
,
,
,
,
,
,并按这样的规律继续下去.给出下列四个结论:
①对于任意正整数
,
;
②存在正整数
,
为整数﹔
③存在正整数
,三角形
的面积为2023;
④对于任意正整数
,三角形
为锐角三角形.
其中所有正确结论的序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d07a71ea5e77168d101526bd081433.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca037c7d1fe65ecce1b461a85e81e66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47e9f1dbb824847e8a2263c53e908f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb45212d451f476d6841e92293dc02da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb355a93c360dc25647040e21e5b5e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1101dbc7953e33c516d7cc282c7842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b995d143c9835dbc38fb9d7c73e3f8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8911915f1df38893bddbd642aaee24.png)
①对于任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b15d53749aac7fe0989915ec7db710.png)
②存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62f2f63fd60956219cc9eac437aebb3d.png)
③存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad64a12f4337c1ce6236b9b2aae324b3.png)
④对于任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad64a12f4337c1ce6236b9b2aae324b3.png)
其中所有正确结论的序号是
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/16/0c32e1c8-c090-4e07-a043-6f16a3f9ef66.png?resizew=170)
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2023-07-10更新
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404次组卷
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2卷引用:北京市第二中学2022-2023学年高二下学期第六学段(期末)考试数学试题
2 . 设
,给出下列四个结论:
①不论
为何值,曲线
总存在两条互相平行的切线;
②不论
为何值,曲线
总存在两条互相垂直的切线;
③不论
为何值,总存在无穷数列
,使曲线
在
处的切线互相平行;
④不论
为何值,总存在无穷数列
,使曲线
在
处的切线为同一条直线.
其中所有正确结论的序号是____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9cc29e5eda42231b07864342ae3469d.png)
①不论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
②不论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
③不论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c447d258d81765005b59ba0b29ab471b.png)
④不论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c447d258d81765005b59ba0b29ab471b.png)
其中所有正确结论的序号是
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3 . 在
中,角
所对的边分别为
,
,且
的面积为
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e2557d6c0eeb8e56c84db1c4931c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f13a05f5aca98574bb1f927123490de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b8b98b2f83279a49e94d9f48c5e6f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc7407d82d6e55b969d34e937ce36f3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
A.![]() | B.5 | C.![]() | D.![]() |
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9卷引用:北京市第五中学2022-2023学年高二下学期期末检测数学试题
北京市第五中学2022-2023学年高二下学期期末检测数学试题宁夏贺兰县第一中学2022-2023学年高一下学期数学期末复习试题(三)河南省新未来2023届高三5月联考文科数学试题(已下线)第4讲 解三角形(1)-《考点·题型·密卷》(已下线)第02讲 解三角形专题期末高频考点题型秒杀(已下线)专题1 平面向量(3)(已下线)专题2 平面向量(2)(已下线)模块一 专题3 解三角形(苏教版)西藏林芝市第二高级中学2023届高三第四次模拟考试数学(理)试题
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解题方法
4 . 如图,在四棱锥
中,底面
是边长为3的正方形,
平面
,点M为底面上的动点,M到
的距离记为d,若
,则点M在底面正方形内的轨迹的长度为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/e7522e7d-3b86-4d1a-8772-8ca5a66c2ee5.png?resizew=179)
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e2de7c6600c3dc4d6a37f382792077.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/e7522e7d-3b86-4d1a-8772-8ca5a66c2ee5.png?resizew=179)
A.2 | B.![]() | C.![]() | D.![]() |
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4卷引用:北京市东城区第一六六中学2023-2024学年高二上学期期末模拟数学试题
5 . 已知函数
,若对于任意
,满足
,且
,则一定有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a08e81373f1299bf69fb54fead8d0798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5223ece2f8f76850c49e2505304532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c2e41c64ac5508a9ba27b697122d6d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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6 . 已知
同时满足下列四个条件中的三个:①
;②
的图象可以由
的图像平移得到;③相邻两条对称轴之间的距离为
;④最大值为2.
(1)请指出这三个条件,并说明理由;
(2)若曲线
的对称轴只有一条落在区间
上,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644dfdf309ed33a2c67896af33bda1ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc8bde4896ae4b9d3403b03f1bed9fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae940a6bbc41da7a81f80ceea5f8c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca2810eb34112a2e9101315c2b9c125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ad72d7565699d1ebb741eb0ce12bac.png)
(1)请指出这三个条件,并说明理由;
(2)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3f7f762131c77a3c8440b4a3bc1d12.png)
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9卷引用:北京市第五中学2022-2023学年高二下学期期末检测数学试题
北京市第五中学2022-2023学年高二下学期期末检测数学试题北京市第二中学2021届高三高考模拟数学试题(已下线)第12课时 课后 函数y=Asin(wx+φ)(已下线)考点15 三角函数的图象与性质-备战2022年高考数学(文)一轮复习考点帮北京名校2023届高三二轮复习 专题二 三角与平面向量 第1讲 三角函数的图象与性质(已下线)第9课时 课后 函数y=Asin(wx+φ)(完成)北京市首都师范大学附属中学(通州校区)2022-2023学年高一下学期开学质量检测数学试题河北衡水中学2023届高三一模数学试题(已下线)第五篇 专题9 逆袭90分综合模拟训练(九)
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7 . 仔细阅读下面三个函数性质:
(
)对任意实数
,存在常数
,使得
.
(
)对任意实数
,存在常数
,使得
.
(
)对任意实数
,存在常数,使得
.
请写出能同时满足以上三个性质的函数(不能为常函数)的解析式__________ .(写出一个即可)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c171d0021b15415b055c223935a2292.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/156d0e8f3176584a06f774a7a15c99ac.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357f35cfcdc9cc8f655290cebaa90bfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a1c02c533c60949a994212c90fbeda.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a0ad869e385be373c7037214397b9e.png)
请写出能同时满足以上三个性质的函数(不能为常函数)的解析式
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8 . 将函数
的图像上所有点的横坐标变为原来的一半,再向右平移
个单位,所得函数的解析式为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
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