名校
1 . 已知函数
,其中
.
(Ⅰ)讨论
的单调性;
(Ⅱ)当
时,证明:
;
(Ⅲ)求证:对任意正整数n,都有
(其中e≈2.7183为自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9f7cb75c5500ad56dfe0f178dedb92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(Ⅰ)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257810d08006d4b886331966c99767ea.png)
(Ⅲ)求证:对任意正整数n,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf0f4b1e329db4bf6070f993297f9b9.png)
您最近一年使用:0次
2019-01-12更新
|
4102次组卷
|
10卷引用:【全国百强校】河北省武邑中学2019届高三下学期第一次模拟考试数学(文)试题
【全国百强校】河北省武邑中学2019届高三下学期第一次模拟考试数学(文)试题【区级联考】天津市蓟州等部分区2019届高三上学期期末联考数学(文)试题【区级联考】天津市部分区2019届高三(上)期末数学(文科)试题江西省五市八校2019-2020学年高三第二次联考文科数学试题黑龙江省大庆实验中学2019届高三普通高等学校招生全国统一考试文科数学模拟试题【全国百强校】四川省成都市成都外国语学校2018-2019学年高二下学期期中考试文科数学试题湖北省武汉二中2019-2020学年高二下学期4月第二次线上测试数学试题四川省宜宾市第四中学校2019-2020学年高二下学期期中考试数学(理)试题四川省宜宾市第四中学校2019-2020学年高二下学期期中考试数学(文)试题广东省佛山市三水区三水中学2019-2020学年高二下学期第二次统考数学试题
解题方法
2 . 过点
可以作曲线
的两条切线,切点为
.
(1)证明:
;
(2)设线段
中点坐标为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bec550c01b4f075f22ab67f5e55ed5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a88cea6e5ba43dd2649f4b4618702b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a0e15c4c7992504099591ad8c23456.png)
(2)设线段
![](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/138dd512203c5b0e038b904ae67762b4.png)
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解题方法
3 . 已知函数
.
(1)求
的值域;
(2)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d85891847e4fce1951f0eb6a5c696c5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c768e5a8a2c72590a83fb7f0b2f10475.png)
您最近一年使用:0次
名校
解题方法
4 . 已知函数
.
(1)若
,求证:
;
(2)若
,试判断函数
在区间
上的零点的个数,并说明理由.(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d87c47a27e28cd26579867e07ee2a6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2bcca35c25a337eab92fd2171a1505f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b76ec9dbfc84cc2d5f257021b725bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71b6baa0ae674754411a821b1bce280.png)
您最近一年使用:0次
2024-01-22更新
|
305次组卷
|
2卷引用:河北省保定市唐县第一中学2024届高三上学期期末数学试题
5 . 已知椭圆
的左右焦点分别为
,点
为椭圆
上异于顶点的一动点,
的角平分线分别交
轴、
轴于点
.
(1)若
,求
;
(2)求证:
为定值;
(3)当
面积取到最大值时,求点
的横坐标
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.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/e6670479a0083dd2dfd5ad55b47b1ab6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e099a6abe3e9566b2ad385906e323fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4ef569668e797b1e94257fd5f4384dd.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/066b9c12f71ed215ed8e98df05584f76.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b0bac6df5da367c886f57d562c72c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
2024-02-12更新
|
1970次组卷
|
4卷引用:专题07 直线与圆、圆锥曲线
解题方法
6 . 已知函数
(e为自然对数的底数).
(1)当
时,求函数
的极值;
(2)证明:
,当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d22bcbdce47d0f4deb1f751deb3aca2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e445f608e4a7d8535b100c0199a8ecf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6422b9c2e93a91fe9e39ce4d9dabb0fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4113cb39760f274b08f5edf0a7d6e1a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408a39bc5127abfbd015a517c2637cf4.png)
您最近一年使用:0次
2023-12-21更新
|
181次组卷
|
3卷引用:河北省沧州市泊头市2024届高三上学期12月联考数学试题
7 . 设
,函数
,其中
.
(1)讨论
的零点个数;
(2)证明:对任意
,都存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c951bbfc72e4d70d7c77be47fb1ba2f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82c4003d20b36777f7aea584e3dd4.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cffdab27a4a79c8da94c0c418ddb1ce.png)
您最近一年使用:0次
名校
8 . 已知函数
,
.
(1)求
的单调区间;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc1e1eda1e062dc9c898622072f0495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1610bcd07b02c4ed7184ad586b88f373.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375d897a1f137d6c6704d24f9b4b0948.png)
您最近一年使用:0次
2023-11-15更新
|
385次组卷
|
5卷引用:河北省沧衡八校联盟2023-2024学年高三上学期11月期中考试数学试题
名校
9 . 已知函数
,
.
(1)讨论
的单调性;
(2)已知
有两个极值点
,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce03d543ae6d19bb0743a53b5f98e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b764a9f6ce514bf09fcdd36c1e66f76.png)
您最近一年使用:0次
2023-11-23更新
|
339次组卷
|
2卷引用:河北省部分高中2024届高三上学期期末数学试题
名校
解题方法
10 . 已知函数
.
(1)若
在
上单调递增,求实数
的取值范围;
(2)若
有两个极值点分别为
,
(
),当
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fd5390482e4ed10943c47fb132f2ac7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](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/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d8047f0a8bd0cf4e250cd0fe80093b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05ec5d2d91935134a0eedd5d51e05212.png)
您最近一年使用:0次
2024-01-19更新
|
242次组卷
|
2卷引用:河北省邢台市2024届高三上学期期末调研数学试题