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 . 已知
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
,求证:
(1)
;
(2)
;
(3)
;
(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c54de16ee463c02d1e26f0a86a4223.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/001ecfa2f7fd551ecf48fd32a1cd3971.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6d9fa392ec880e0e590bd1a90599e92.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291d415ccb6166e7af7a5d98a5998504.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68aef48075c9b177803def07ac6cf99d.png)
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2023-10-09更新
|
170次组卷
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3卷引用:北师大版(2019)必修第二册课本习题 习题5-2
3 . 已知复数z满足
,求证:
是实数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70c2519610d6d1d6d0855b0f27dfc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ae50806d8c14f0275864b30e9f30a7.png)
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解题方法
4 . (1)已知复数
的实部与虚部互为相反数,求
;
(2)已知复数
满足
,求证:
是实数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1eb7d9214d88209502cf9464910ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de971553ea8a66d7849b138a4a0625c5.png)
(2)已知复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b70c2519610d6d1d6d0855b0f27dfc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ae50806d8c14f0275864b30e9f30a7.png)
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解题方法
5 . 已知
是虚数,且
是实数,求证:
是纯虚数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ae50806d8c14f0275864b30e9f30a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd149f07fc77d1a32b9ed4d40737e71.png)
您最近一年使用:0次
名校
解题方法
6 . 已知复数
满足
.
(1)求
的最小值与最大值;
(2)若z所对应的点在第一象限,且
为实数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78b78b8fe7da9e76822d85a2a0336484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ec00601d3297c94a1a224421df7d1d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48c344fd5607cb7a3ce319165fbf45f8.png)
(2)若z所对应的点在第一象限,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59ae50806d8c14f0275864b30e9f30a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fa4b7b50a233a09e7da199f75bc9dc.png)
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2023-05-10更新
|
173次组卷
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2卷引用:陕西省咸阳市武功县2022-2023学年高二下学期期中文科数学试题
解题方法
7 . 设
是虚数,
是实数且
.
(1)求
的值以及
实部的取值范围;
(2)若
,求证:
为纯虚数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/174ce5fa8bd9b7c64f634c73f8e1c238.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc19635488613e74ef7d770adcf9154.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8b3f66119c2ce542984d12eb2b6b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caf365042ac7c12643eac7c75a0fafad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
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名校
解题方法
8 . 已知虚数z满足
.
(1)求证:
在复平面内对应的点在直线
上;
(2)若
是方程
的一个根,求
与
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/128cf2d830a0be68857f24280da22895.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77fe88a4d87ed5872ebb847412619ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1e51427c2d933bb6466973b44dd9627.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
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2023-03-27更新
|
628次组卷
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4卷引用:河南省洛阳市强基联盟2022-2023学年高一下学期3月月考数学试题
河南省洛阳市强基联盟2022-2023学年高一下学期3月月考数学试题河北省承德市重点高中2022-2023学年高一下学期期中联考数学试题(已下线)12.3 复数的几何意义(2)-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(苏教版2020必修第二册)江西省赣州市大余县九师联盟联考2022-2023学年高一下学期5月月考数学试题
9 . (1)已知
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
,求证:
;
(2)求函数
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41c54de16ee463c02d1e26f0a86a4223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf429c713e453aa6f0b80761e5af0329.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7cc4ebce6704adf082e6040762250f8.png)
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2023-02-06更新
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295次组卷
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6卷引用:沪教版(2020) 一轮复习 堂堂清 第六单元 6.4 复数的运算
沪教版(2020) 一轮复习 堂堂清 第六单元 6.4 复数的运算(已下线)第七章《复数》同步单元必刷卷(培优卷)-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)7.2.1 复数的加、减运算及其几何意义-高一数学同步精品课堂(人教A版2019必修第二册)(已下线)7.2.1复数的加、减运算及其几何意义【第三练】“上好三节课,做好三套题“高中数学素养晋级之路(已下线)7.2.1?复数的加、?减运算及其几何意义——课后作业(提升版)(已下线)7.2.1?复数的加、?减运算及其几何意义——课后作业(巩固版)
10 . 已知非零复数
,
满足
,求证:
一定是负数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093613ea9152eb78b80f82a05f169735.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2a89199dc1814ed98ee1e7f2b3ea477.png)
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