名校
解题方法
1 . 已知函数
.
(1)当
时,求证:
;
(2)当
时,
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0aae5dab128ab12ff005b8d4e07a0f9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad5ed9610121bb275c4a40205c76c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2021-06-28更新
|
1392次组卷
|
12卷引用:安徽省合肥六中2021届高三6月份高考数学(理)模拟试题
安徽省合肥六中2021届高三6月份高考数学(理)模拟试题吉林省长春市实验中学2020-2021学年高二下学期期末考试数学(文)试题安徽省合肥市第六中学2021-2022学年新高三上学期6月月考理科数学试题陕西省汉中市十三校2021-2022学年新高三6月摸底联考理科数学试题辽宁省名校2022届高三第五次联合考试数学试题云南省文山州2020-2021学年高二下学期期末考试数学(文)试题浙江省“南太湖”联盟2021-2022学年高二下学期第一次联考数学试题广东省广州市天河中学2021-2022学年高二下学期期中数学试题浙江省杭州市第九中学2021-2022学年高二下学期期中数学试题(已下线)专题10 导数及其应用 -3河南省洛阳市2022-2023学年高二下学期期中考试数学(文)试题河南省洛阳市2022-2023学年高二下学期期中考试数学试题(理)
2 . 已知函数
.
(1)求证:
;
(2)求证:对于任意正整数
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3aef5ae7abef0e3ecba1c6a39e5fa5.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)求证:对于任意正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf0f4b1e329db4bf6070f993297f9b9.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)若
恒成立,求实数
的取值范围.
(2)若函数
的两个零点为
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e652627c6c83c132e152f410e82f8285.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28190cf04b0340966281667797469291.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/1b4900c67f4b57fa430c4bd863f8e896.png)
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2021-07-08更新
|
3397次组卷
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12卷引用:河北省部分名校2020-2021学年高二下学期期末联考数学试题
河北省部分名校2020-2021学年高二下学期期末联考数学试题黑龙江省大庆中学2021-2022学年高三上学期开学考试数学(文)试题湖南师范大学附属中学2021-2022学年高三上学期第二次月考数学试题安徽省合肥市第一中学2021-2022学年高三上学期段一测试理科数学试题湖南师大附中2022届高三上学期月考数学试题(二)(已下线)专题07 极值点偏移问题-【解题思路培养】2022年高考数学一轮复习解答题拿分秘籍 (全国通用版) (已下线)2022届高三普通高等学校招生全国统一考试数学信息卷(八)湖南省长沙市长郡中学2021-2022学年高二上学期期末数学试题福建省龙岩第一中学2021-2022学年高二下学期第一次月考数学试题辽宁省铁岭市昌图县第一高级中学2021-2022学年高二下学期期末数学试题江苏省宿迁市北大附属宿迁实验学校2022-2023学年高三上学期11月期中数学试题江苏省盐城市东台创新高级中学2022-2023学年高二下学期2月月检测数学试题
4 . 已知双曲线的左,右焦点分别为
,
,离心率
,且过点
.
(1)求双曲线的标准方程;
(2)直线
与双曲线交于M,N两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5641df2cf6ae774d06733a2f73172a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2776e22e73b1bf3914056e1fa2aa3a.png)
(1)求双曲线的标准方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36aa6059d86873be18cb1e50bcb3465a.png)
您最近一年使用:0次
2021-01-17更新
|
203次组卷
|
2卷引用:甘肃省白银市会宁县2020-2021学年高二上学期期末考试数学(文)试题
名校
解题方法
5 . 已知点
、
为双曲线
的左、右焦点,过
作垂直于x轴的直线,在x轴上方交双曲线C于点M,且
,圆O的方程是
.
(1)求双曲线C的方程;
(2)过双曲线C上任意一点P作该双曲线两条渐近线的垂线,垂足分别为
、
,求证:
为定值;
(3)若过圆O上点
作圆O的切线l交双曲线C于A、B两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/176569a223942b06f78d81633e2467b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f47f9dfaf412d7e5d6e47e81826d4b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.png)
(1)求双曲线C的方程;
(2)过双曲线C上任意一点P作该双曲线两条渐近线的垂线,垂足分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e25025b70318f4e98f901db9ba489740.png)
(3)若过圆O上点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2752e086b85f9fbb95010bf771072af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
您最近一年使用:0次
20-21高二下·浙江·期末
6 . 已知函数
.
(Ⅰ)讨论函数
的单调性;
(Ⅱ)若函数
有两个零点
,
(ⅰ)求a的范围;
(ⅱ)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575eaafd1bebccfd6b10b71a9814c658.png)
(Ⅰ)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
(ⅰ)求a的范围;
(ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5120da38792c0c52a5f54cc7912e290f.png)
您最近一年使用:0次
解题方法
7 . 已知
(
)的顶点
与焦点
,
构成面积为1的直角三角形.
(1)求椭圆
的方程;
(2)若直线
(
)与椭圆
相交于
,
两点,且
的垂直平分线过点
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0fe9059acc47d2447576e1260c4622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/749b71e49c95b9212a600e837261ccdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e79a22744f10a78ec680f6a8d9ad7df.png)
您最近一年使用:0次
20-21高二下·浙江·期末
解题方法
8 . 已知曲线
与曲线
在公共点
处的切线相同,
(1)求实数a的值;
(2)求证:
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e5bc13dc56819623665ea607c7b5e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c067e6d907f6c0fdfa9be70bbc027595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
(1)求实数a的值;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/498912eb7353a5e918421393e8bf70a7.png)
您最近一年使用:0次
解题方法
9 . 已知函数
.
(1)若
时,
恒成立,求
的取值范围;
(2)求证:
(
且
);
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbd2ea1035a786f94df7092aa7228280.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9385741d263b30b28dd246d086c59260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
您最近一年使用:0次
10 . 已知正数
,
满足方程
.
(1)若
,求证:方程有且只有一个实数解.
(2)当
时,求证:
;
(3)求证:
.
参考数据:
,
.
![](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/d319a99df9a9881db7e7d65ee0c65903.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07b9d5aaaceaa3ac514d17fcfefbf9b4.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec336faee8689281a6f6b465e7fcff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e29d9430326bf1794e23077e89d47a3.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a79d7f73b6128650bf7aed538260c72.png)
参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405361d7be3c9e4d462a4e955d8fe3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af36b8a5f7fb24a5b7ea1f46ac92b886.png)
您最近一年使用:0次