名校
解题方法
1 . 设复数
,m为实数.
(1)当m为何值时,z是纯虚数;
(2)若
,求
的值;
(3)若复数
在复平面内对应的点在第三象限,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c3c97f13b08800501e2814c075ac97.png)
(1)当m为何值时,z是纯虚数;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0db2c49919467a2e14540f2aabd05cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c042c0c7e253a65f770583c5c6696770.png)
(3)若复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d41042207515dd2e8349c805e6aee400.png)
您最近一年使用:0次
2023-05-12更新
|
1791次组卷
|
8卷引用:浙江省杭师大附2022-2023学年高一下学期期中数学试题
浙江省杭师大附2022-2023学年高一下学期期中数学试题(已下线)第03讲 复数专题期末高频考点题型秒杀江西省部分学校2022-2023学年高一下学期5月月考模拟数学试题天津市和平区2022-2023学年高一下学期期末数学试题(已下线)专题12 复数的概念及几何意义-《重难点题型·高分突破》(苏教版2019必修第二册)山东省菏泽市思源学校2023-2024学年高一下学期数学第一次月考(4月)数学试题(已下线)专题01 复数-《期末真题分类汇编》(天津专用)(已下线)专题02 复数-《期末真题分类汇编》(新高考专用)
2 . 设
,已知函数
有
个不同零点.
(1)当
时,求函数
的最小值:
(2)求实数
的取值范围;
(3)设函数
的三个零点分别为
、
、
,且
,证明:存在唯一的实数
,使得
、
、
成等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0561c7ee9cc57163dc269b636af6366e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3ff82555cd8d9ee3046931a5d953603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbed74d1e10a5636b0b62a09ac00933f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
您最近一年使用:0次
解题方法
3 . 设函数
,其中
.
(1)当
时,求函数
的值域;
(2)设
,当
时,
①证明:函数
恰有两个零点;
②若
为函数
的极值点,
为函数
的零点,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e1acdff0e8b184f4e5b6d9809488c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e15c2171c1be9ec394494ad822a048d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
①证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64df36fd0b37b72d36fe21e10f5d67f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70cbfe220a84f9bc9ddfd9f4c56041e.png)
您最近一年使用:0次
名校
解题方法
4 . 已知
.
(1)若
,且
对任意
恒成立,求a的范围;
(2)当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522a34276b4c878223d7cd45b49a45a9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/238df5f9ba4a92e3b6ee522b93550db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2085ce588f4a4cc389c5678e2ee12d71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb279630c002eec7ea4a2a711134fb74.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e07d5d11e230bf6e22a0317abbca335.png)
您最近一年使用:0次
2023-05-11更新
|
418次组卷
|
3卷引用:浙江省嘉兴市海盐第二高级中学2022-2023学年高二下学期期中数学试题
名校
解题方法
5 . 已知函数
.
(1)若
,求
的单调区间;
(2)若关于x的不等式
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92198a8d10a82bc926eab1edab325307.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cff79947f37b65163df685e23cc3828e.png)
您最近一年使用:0次
6 . 已知函数
.
(1)若
恒成立,求
的取值范围;
(2)当
时,若
,其中
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd717b493c9813275401d605083da0be.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2160006cea5957846b98162937faa6d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e4ae07b78add20468f66fcf3a7ddb2.png)
您最近一年使用:0次
7 . 已知过点
可以作曲线
的两条切线,切点分别为
、
,线段
的中点坐标为
,其中
是自然对数的底数.
(1)若
,证明:
;
(2)若
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bec550c01b4f075f22ab67f5e55ed5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d0755975f77eae028bc83b6f3675818.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a262d480584627cf6692ff7685dd130.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e84dbb03e8c627ff11d5c7aeb0c8b5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a4eaa80b44625890339d6a0065c241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0679dfbe17ec46921d41391a91d1aec1.png)
您最近一年使用:0次
名校
8 . 已知函数
,a为实数.
(1)求函数
的单调区间;
(2)若函数
在
处取得极值,
是函数
的导函数,且
,
,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff3e03104de1a98c25ca84bd9591a31.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187c21027ff08411931d32c530b64fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb8a229cc42ec3bc9c5e68523cf5ebbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d24e9b3a955613bcb1a4fd32ab64c341.png)
您最近一年使用:0次
2023-05-08更新
|
1296次组卷
|
5卷引用:浙江省绍兴市柯桥区2023届高三5月高考及选考科目适应性考试数学试题
浙江省绍兴市柯桥区2023届高三5月高考及选考科目适应性考试数学试题湖北省武汉市第六中学2022-2023学年高二下学期第四次月考数学试题黑龙江省牡丹江市第一高级中学2023届高三热身考试(二)数学试题(已下线)重难点突破05 极值点偏移问题与拐点偏移问题(七大题型)-1(已下线)重难点06 导数必考压轴解答题全归类【十一大题型】
9 . 已知函数
.
(1)若
,求
的单调区间;
(2)证明:
;
(3)若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bca2ea44773445d05136ca960f803b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de16252e1fb8e30a5111572a8f69fcb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1a2c01ac2a7f6ad7e03cb7a61daefab.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f81cdc2ba46f6aeb3bb9a76e065b9755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数
.
(1)证明:函数
在
上有且只有一个零点;
(2)当
时,求函数
的最小值;
(3)设
,若对任意的
恒成立,且不等式两端等号均能取到,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0efc5fda061b4ed54baebd31ae741d.png)
(1)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a90f71a22daa4df7bd75c1e3e66fcb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d795e3d9afa935e2741c75526a8c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adae3f8382c7456d50855aaf9a12b37f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
您最近一年使用:0次
2023-05-06更新
|
2124次组卷
|
6卷引用:浙江省温州市2023届高三下学期5月第三次适应性考试(三模)数学试题
浙江省温州市2023届高三下学期5月第三次适应性考试(三模)数学试题广东省深圳外国语学校2022-2023学年高二下学期期末数学试题江西省南昌市新建区第二中学2024届高三上学期8月开学学业水平检测数学试题(已下线)专题05 导数大题上海外国语大学附属浦东外国语学校2024届高三下学期3月月考数学试题(已下线)高二数学下学期期末押题试卷02(测试范围:新高考全部内容)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(新高考专用)