1 . 对于函数
,分别在
处作函数
的切线,记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”,同理记切线与
轴的交点分别为
,记
为数列
的第n项,则称数列
为函数
的“切线-
轴数列”
(1)设函数
,记
“切线-
轴数列”为
,记
为
的前n项和,求
.
(2)设函数
,记
“切线-
轴数列”为
,猜想
的通项公式并证明你的结论.
(3)设复数
均为不为0的实数,记
为
的共轭复数,设
,记
“切线-
轴数列”为
,求证:对于任意的不为0的实数
,总有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ed953d6e0bd80a5da66552c7bfbcbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3d48fa9493a86f262569df235a82ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8292395dc894796602a60486e575a808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a79b9eaa5e7ab7a1e5c512b571914dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36460040ddea4761eee10d537b14a1f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ef5756fec38d1b4dc62358b45c3352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10e845964df4b271bd7b4cf99ede79be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028517e8bebe634441e0a5c79828e88a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
(3)设复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80bcf306a6aa8554d1d7fc8317f4e946.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fcfebd9f5a57036e6df6b6e14865da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec5f303f666e164582da05968d9d8cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18c49ca8562b98657ca9c499093f7233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6f044a9b06a7a769e613c977cbfb87.png)
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2024-01-01更新
|
443次组卷
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7卷引用:上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题
上海市普陀区桃浦中学2022-2023学年高二下学期期中数学试题(已下线)模块一专题1【练】《导数的概念、运算及其几何意义》单元检测篇B提升卷(人教A2019版)(已下线)模块二 专题1 与曲线的切线相关问题(已下线)模块二 专题3 与曲线的切线相关问题(人教B版)(已下线)模块一 专题1 《导数的概念、运算及其几何意义》B提升卷(苏教版)(已下线)模块二 专题1 与曲线的切线相关问题(苏教版高二)(已下线)模块二 专题4 与曲线的切线相关问题(高二北师大版)
2 . 设z是虚数,在平面直角坐标系xOy中,z,
,
对应的向量分别为
,
,
.
(1)证明:O,B,C三点共线;
(2)若
,求向量
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41042207515dd2e8349c805e6aee400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1245ed74a632317d3a0a106aa9d02eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8337706c550bc095d7a2bd872221a1.png)
(1)证明:O,B,C三点共线;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877f1a7e02a675480afc50d144782c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e973a6cfc29bbeade6d6654d286b5c22.png)
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3 . 求证:若复数
,则z为纯虚数的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ece25234a41280cbd80226680cdb0f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d94c298068bb7faf44819e028d6960b5.png)
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2021-11-02更新
|
389次组卷
|
5卷引用:第十章 复数 10.2 复数的运算 10.2.2 复数的乘法与除法
(已下线)第十章 复数 10.2 复数的运算 10.2.2 复数的乘法与除法人教B版(2019) 必修第四册 逆袭之路 第十章 10.2 复数的运算小结(已下线)第3课时 课中 复数的加法、减法运算(已下线)7.2.1 复数的加、减运算及其几何意义(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)人教B版(2019)必修第四册课本习题习题10-2
4 . 已知复数
,
为
的共轭复数.
证明:(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20129f794f91bd4f2c135036289d44a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41042207515dd2e8349c805e6aee400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
证明:(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be148e4930f353264a8e1b62e81f5be.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877f1a7e02a675480afc50d144782c16.png)
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5 .
,求证:
的充分必要条件是
,
中至少有一个为1.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea77b7c1c49d58da6fbaf2890c65634a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/523c7ea7352bd6b81578373bce98ab24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8b3f66119c2ce542984d12eb2b6b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dff9388eee5c812d183b254d13f461b.png)
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6 . 已知复数
,
,
是虚数单位.
(1)求证
;
(2)若
为实数,求实数
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6741b8baeeefa7a684e30bd1b4a037c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a17d6a58ebaf3376a3348f0384474f3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/998981081c91fbf632aae04c813892ad.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec04f844e8fd9d9b1ef835e23eaa54e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2021-08-20更新
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132次组卷
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2卷引用:江苏省泰州市靖江市2020-2021学年高二下学期期中数学试题
20-21高二·全国·单元测试
解题方法
7 . 已知复数
,若存在实数
,使
成立.
(1)求证:
为定值;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/563edadd6a6cbc8516a72241048e72dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c09f7d1b82ef2cfccb561ad49f9d948.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0113fd4c7d157757571f9a009e02af.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/159f9d0fa8432510d4d6ad90172c6c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de971553ea8a66d7849b138a4a0625c5.png)
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8 . 复数
,存在实数
,使
成立.
(1)求证:
为定值;
(2)求
的取值范围
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b043be463a12c01175d22d744aa20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e009cb31fc7d1f9149d3c6c6434dde0.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0113fd4c7d157757571f9a009e02af.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de971553ea8a66d7849b138a4a0625c5.png)
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9 . 求证:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/622e0a3909431492467887938381948e.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e7f128ae66083e4903356279a85bf7.png)
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2020-01-31更新
|
181次组卷
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3卷引用:第十章 复数 10.2 复数的运算 10.2.1 复数的加法与减法
(已下线)第十章 复数 10.2 复数的运算 10.2.1 复数的加法与减法人教B版(2019) 必修第四册 逆袭之路 第十章 10.2.1 复数的加法与减法人教B版(2019)必修第四册课本习题10.2.1 复数的加法与减法
10 . 求证:
(1)
;
(2)
;
(3)
;
(4)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411d0fec78c98dda7eb2e048df7d1b40.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea42cfc60639a2634a729e7a120152c.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694edfed19f6c329e360bf2bef4e23d7.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4695e20874a7ce9d94c3fc1d5f4504.png)
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2020-01-30更新
|
1271次组卷
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6卷引用:第十章 复数 10.2 复数的运算 10.2.2 复数的乘法与除法
(已下线)第十章 复数 10.2 复数的运算 10.2.2 复数的乘法与除法人教B版(2019) 必修第四册 逆袭之路 第十章 10.2.2 复数的乘法与除法(已下线)第19讲压轴综合题(讲义)-【教育机构专用】2021年春季高一数学辅导讲义(沪教版2020必修第二册)(已下线)专题05 复数压轴题型汇总-2021-2022学年高一《新题速递·数学》(人教A版2019)人教B版(2019)必修第四册课本习题10.2.2 复数的乘法与除法(已下线)第七章 复数(基础、典型、易错、压轴)分类专项训练(2)