1 . 已知椭圆
的左右顶点分别为A,B,点P为椭圆上异于A,B的任意一点.
(1)证明:直线PA与直线PB的斜率乘积为定值;
(2)设
,过点Q作与
轴不重合的任意直线交椭圆E于M,N两点.问:是否存在实数
,使得以MN为直径的圆恒过定点A?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ca510ef067eec33d821b6ae812f4f8.png)
(1)证明:直线PA与直线PB的斜率乘积为定值;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dabd18bfe473568dc03b825e0d2700a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数
,
,
.
(1)当
,
时,求证:
;
(2)若
恒成立,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41390c499f3dcec5e7122a96f30915af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eecdb2efe6f97677647ab673dfd4256.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2cbbf4d5b8ecbfccc5de39781396d07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
您最近一年使用:0次
2021-05-12更新
|
1180次组卷
|
6卷引用:广西南宁市第三中学2021届高三收网考数学(理)试题
广西南宁市第三中学2021届高三收网考数学(理)试题广西梧州市黄埔双语实验学校2022届高三上学期期中考试数学(理)试题安徽省安庆市2021届高三下学期二模理科数学试题(已下线)第19讲 不等式恒成立之双变量最值问题-突破2022年新高考数学导数压轴解答题精选精练河南省示范性高中2021-2022学年高三下学期阶段性模拟联考三理科数学试题贵州省兴义市第八中学2024届高三上学期第八次月考数学考试题
解题方法
3 . 已知a>0,函数
.
(1)若f(x)为减函数,求实数a的取值范围;
(2)当x>1时,求证:
.(e=2.718…)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54648bc725c96f7344549d79161bd154.png)
(1)若f(x)为减函数,求实数a的取值范围;
(2)当x>1时,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4720f9f8840de5108a124e817b85de2.png)
您最近一年使用:0次
2020-11-22更新
|
1386次组卷
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2卷引用:广西梧州市2021届高三3月联考数学(理)试题
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b59895e7a9601606cf61f271d20cc92.png)
.
(1)求
的单调区间;
(2)证明:(i)
;
(ii)
.
(备注:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b59895e7a9601606cf61f271d20cc92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/118c9c0597d2c72126fbc4cc3927108e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/102f2455ccfb30b7da355988ab14f5c1.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd3134b781f6191132c463216e211629.png)
(备注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/349ebea3bf2d62e39d595cc9499ccf13.png)
您最近一年使用:0次
5 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a32dd8c3c4a3bc3fff0757544cf38b2.png)
(1)当
时,判断
的单调性;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a32dd8c3c4a3bc3fff0757544cf38b2.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b108ab31cc093f03cf48ad65429889e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d92d829236f3c177e643f00e4bef05.png)
您最近一年使用:0次
2020-01-04更新
|
499次组卷
|
2卷引用:广西玉林市第十一中学2022届高三9月月考数学(文)试题
名校
6 . 已知函数
,
.
(1)若
存在极小值,求实数
的取值范围;
(2)设
是
的极小值点,且
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/160602a87d2645363d45ec59bba246e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc8ecf91d5a295bd998eed6d1c64886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1148acb0b4fd538a15857fdda4f6efb4.png)
您最近一年使用:0次
2019-05-14更新
|
1861次组卷
|
6卷引用:广西玉林市2021届高三11月期末数学(理)试题