名校
1 . 对于函数
,若在其定义域内存在实数
,t,使得
成立,称
是“t跃点”函数,并称
是函数
的“t跃点”.
(1)若函数
,x∈R是“
跃点”函数,求实数m的取值范围;
(2)若函数
,x∈R,求证:“
”是“对任意t∈R,
为‘t跃点’函数”的充要条件;
(3)是否同时存在实数m和正整数n使得函数
在
上有2021个“
跃点”?若存在,请求出所有符合条件的m和n的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a51859654d92b5a713bea964091caf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc53b0c595360667740141eb101d2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/981b69bdf68d1e6ed203759d596cd5ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da5bdf99eba8520b6ec1fc7567900db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)是否同时存在实数m和正整数n使得函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb853095f13ee953f77e788f9b75258f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84c6c1e0ea3b81713db2f764eba0e251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
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2022-04-25更新
|
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|
7卷引用:上海市奉贤中学2021-2022学年高一下学期线上教学调研检测数学试题
上海市奉贤中学2021-2022学年高一下学期线上教学调研检测数学试题(已下线)专题01 集合与逻辑(练习)-2(已下线)第1章 集合与逻辑(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高一数学考试满分全攻略(沪教版2020必修第一册)上海市青浦高级中学2022-2023学年高一下学期期中数学试题(已下线)第5章 三角函数(基础、典型、易错、压轴)分类专项训练(1)(已下线)第四章 综合测试A(基础卷)黑龙江省牡丹江市第一高级中学2022-2023学年高一上学期期末考试数学试题
2 . 分式线性变换又称为莫比乌斯变换,它是定义在复数集中形如
的变换,其中w称为z的“像”,z称为w的“原像”.
(1)若
,求i的“像”以及
“原像”;
(2)若
,
,求证:
的充要条件是
;
(3)若
,
,z满足
,求z的“像”在复平面上所构成图形的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7192583ba609cb106ade4e4488dd15.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49800f57be0280b700ec3e43a5c81449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186bb9626ba707655b540871c863bdc4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c2c9d5ac204f207fc4edfd2160e7b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa828aaf76504bf5e4a749e28ff3815f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f525f4df6befc8fcf566d6f4f7d2150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/475e17c54117d4b846275df1ba74b26a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adebd26bdc1c9f97d05f111fb22b1073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b83b93d6b7241c2db386d5571b9932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88fe440162463512c88bb099ea959ff.png)
您最近一年使用:0次
2022-04-25更新
|
511次组卷
|
2卷引用:上海交通大学附属中学2021-2022学年高一下学期期中数学试题
3 . 若
,
,求证:
的充要条件是
与
垂直.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500b8c2872cf9cc227fe23911a842534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4714dcba1c087664ecbf4e2011c492.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05f1d68b133c5d2f76a06186e0ffb08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec655f610928ca21831e26645a21e99c.png)
您最近一年使用:0次
4 . 已知函数
.
(1)判断“
为偶函数”是“
”的什么条件?
(2)证明:
为奇函数的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670cf45fa88b684a532253a9e08e99bf.png)
(1)判断“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b1fbd56bd26d659c14b0dd4c2289df.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240fa6e7e7eb945b1a01135b8095bd8d.png)
您最近一年使用:0次
2021-03-25更新
|
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|
2卷引用:沪教版(2020) 必修第二册 同步跟踪练习 第7章 三角函数 7.2.2 第2课时 余弦函数的奇偶性和单调性
5 . 若函数
满足“存在正数
,使得对定义域内的每一个值
,在其定义域内都存在
,使
成立”,则称该函数为“依附函数”.
(1)分别判断函数①
,②
是否为“依附函数”,并说明理由;
(2)若函数
的值域为
,求证:“
是‘依附函数’”的充要条件是“
”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.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/9813ba347d835df2bda3f491e4af1a82.png)
(1)分别判断函数①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6881a170f6ef9ed5c133b95c2f448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a981aa485843b0c1c197937a1400d026.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14f97c1fef6dea43a9cb106a13c5760.png)
您最近一年使用:0次
6 . 对于定义域为R的函数
,若函数
是奇函数,则称
为正弦奇函数.已知
是单调递增的正弦奇函数,其值域为R,
.
(1)已知
是正弦奇函数,证明:“
为方程
的解”的充要条件是“
为方程
的解”;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278220a216c6b4b0656acc01484a5a97.png)
,求
的值;
(3)证明:
是奇函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/181def204e869738a2f39f87a5818be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104375baf5cef5eb92cfc7cf13b80193.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dde0f01007fc21d40fab9b8c8d2521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dbaaee3ba57fa0892b185b243b5c39c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991c3d6d8843ad321f31655c63d42d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7649ab6e2530a885646af610f54ad694.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278220a216c6b4b0656acc01484a5a97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe4b2c42caef444867e0dadd10bccdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
名校
7 . 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)
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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
8 . [选修4-5:不等式选讲]
已知函数
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/475596da-dd66-4b65-93b1-54e77df6d311.png?resizew=191)
(1)在如图所示的网格纸中作出函数
的图象;
(2)记函数
的最小值为
,证明:不等式
成立的充要条件是
.
已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06451202e3a4a67b80d6fbcffd05b068.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/475596da-dd66-4b65-93b1-54e77df6d311.png?resizew=191)
(1)在如图所示的网格纸中作出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f00a712bc86e4ab618694e1c487c744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073bc60dd2b59b2dd928590b8bd85ebe.png)
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2019-04-07更新
|
536次组卷
|
5卷引用:【市级联考】河南省焦作市2019届高三第三次模拟考试数学(理科)试题
9 . 给定数列
,对
,该数列前
项的最大值记为
,后
项
的最小值记为
,
.
(1)设数列
为3,4,7,5,2,写出
,
,
,
的值;
(2)设
是
,公比
的等比数列,证明:
成等比数列;
(3)设
,证明:
的充分必要条件为
是公差为
的等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec41ff7fcb1c4fba6d30a8910fbe165c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f99d7c559ba0656046e63ab35da318f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce0f79b839f7642d567eb760b60b5e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5cbb18c252c89d040dbef1273d7c467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4976fe763ff8c9c5a893f28064d73803.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94aa24198151207cd2e003662419d50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048c8117488725891c92f1db3c5af9a6.png)
(1)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2ec2cccb424df49c89a1348ad6f285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ccdcfb8804ad9c77ffc2fc91eeb4d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61264cdd877b6db34d3f4a400bb52d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a99a84125bd89092d151118e9ad07a1.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dedc3eae16d98d5c5e5108c187d43bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc49fb6f3d806949ad10b7826b0969a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f2ae5cf66f4a16b6fff8277f76a6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cb11ac8d295455a7a2747e168dc488.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8aa5c24766744e194574d31ca534c18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba77c7f6cf14b8dc3415f1b4572af8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29518f13a1ebc3fff8181c2d7cfba22f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
10 . 设
是首项为
,公比为
的等比数列.
(1)若
,
,证明
为单调递增数列;
(2)试探究
为单调递增数列的充要条件(用
和
表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f45f5bc7c648c0e8924b4fa7b1ad08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)试探究
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