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1 . 下列命题正确的有:________ .
①
;
②已知
,若
,则
.
③用反证法证明“已知
,且
,求证:
.”时,应假设“
且
”;
④命题“若
,则
”的逆否命题是“若
,则
”.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d06a4bdf067ee8c14ce02d71271ddf.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eecb11de93939d81b65541b0bbdeb7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8efd32ba5030535598e979fd6d3a4d5c.png)
③用反证法证明“已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c988d709ba8cd8aed6cb83d76c0ba89c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5977232839b54df456aeeacb13512d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c412d5329ba909164329663b7eecdfe.png)
④命题“若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fdf7d28b97fb6fe731703f80e122ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e30c903d8f8a05332af0b19e7e40df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8a2a94168af9b16ce89271a5d8dc6b.png)
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解题方法
2 . 在平面直角坐标系
中,对于直线
和点
、
,记
,若
,则称点
、
被直线
分隔,若曲线
与直线
没有公共点,且曲线
上存在点
、
被直线
分隔,则称直线
为曲线
的一条分隔线.
(1)判断点
是否被直线
分隔并证明;
(2)若直线
是曲线
的分隔线,求实数
的取值范围;
(3)动点
到点
的距离与到
轴的距离之积为
,设点
的轨迹为曲线
,求证:通过原点的直线中,有且仅有一条直线是
的分隔线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29fa0e0526598c4140789f6328daac9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3653fe002a6d9968d6b1d2e7ec36d178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4869bf9983f59598ca7954fd7e89b66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b3d5b330a1e9746267f1a80482e435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a93e8201cd8010f841a105bc9afd99.png)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)判断点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a76e726cd6ff947e0ae20c07ebfa8bf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac02a054bd0771a56987af33454baaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348aca26e61218d251581e21c1129a8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b378e03d75c73c8ca71f991a8c07729a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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20-21高一上·全国·课后作业
3 . 已知ab≠0,求证:a+b=1是a3+b3+ab-a2-b2=0的充要条件.(注意:从充分性、必要性两方面证明.)
您最近一年使用:0次
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4 . (1)已知m是实数,集合
,
.求证:“
”是“
”的充要条件.
(2)设
.证明:若
是奇数,则n也是奇数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0274ba49bbad8b3179d628e3d7025cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e6e153c5b9e2e807125326fd904644c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e851796d98eb47a8d17f4e1b4cea196.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f02d5c8eec434a3f90348d770a2e2b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ceef1abeeef220b4fe5f7d96feedd90.png)
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2020-10-27更新
|
460次组卷
|
8卷引用:上海奉贤区致远高级中学2020-2021学年高一上学期10月月考数学试题
上海奉贤区致远高级中学2020-2021学年高一上学期10月月考数学试题上海市奉贤区致远高级中学2021-2022学年高一上学期10月评估数学试题(已下线)1.2 充分条件与必要条件(第2课时)上海市奉贤区致远高级中学2022-2023学年高一上学期10月月考数学试题(已下线)上海市华东师范大学第二附属中学2022-2023学年高一上学期9月月考数学试题(已下线)1.4 充分条件与必要条件(5大题型)精练-【题型分类归纳】(已下线)专题04充分条件与必要条件-【倍速学习法】(人教A版2019必修第一册)(已下线)专题04常用逻辑用语-【倍速学习法】(沪教版2020必修第一册)
名校
5 . 已知函数
.
(1)判断
的奇偶性并证明;
(2)求证:
在
上是减函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5347d53d531d6378e70f8b4d5a6906c.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a7a4a037a4dfe973f1eb683d93d799.png)
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解题方法
6 . 已知椭圆
,点A、点B分别是椭圆上关于原点对称的两点,点P是椭圆上不同于点A和点B的任意一点.
(1)求证:直线PA的斜率与直线PB的斜率之积为定值,并求出该定值;
(2)试对双曲线
写出具有类似特点的正确结论,并加以证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
(1)求证:直线PA的斜率与直线PB的斜率之积为定值,并求出该定值;
(2)试对双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
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7 . 已知
是实数,求证:
成立的充分条件是
,该条件是否为必要条件?试证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15bd315b801f71bc30b8d772098614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/151cc49463cc25a6a24b9c18c2f4ecea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/648c105b16b56f5484da3def41aa9d70.png)
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2019-09-19更新
|
468次组卷
|
4卷引用:北师大版 新教材 2.1必要条件与充分条件2
8 . 已知函数
的定义域是
且
,
,当
时,
.
(1)求证:
是奇函数;
(2)求
在区间![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bce7c5de6e43a203eb98a7c23f8985.png)
)上的解析式;
(3)是否存在正整数
,使得当x∈
时,不等式
有解?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://img.xkw.com/dksih/QBM/2015/7/3/1572163784851456/1572163790241792/STEM/a51771f539164b6e9d9eead0303f5eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cda1d250b465616dbc1fd75a2359c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c3cfe479362ebb78ff9951d1d9f083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6c48591cae0bcf7ae6c8d589527c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc4e3775c850f1c1804f9eb7a70153a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09bce7c5de6e43a203eb98a7c23f8985.png)
![](https://img.xkw.com/dksih/QBM/2015/7/3/1572163784851456/1572163790241792/STEM/0e39cf5721f84387a7307e4ae19b2041.png)
(3)是否存在正整数
![](https://img.xkw.com/dksih/QBM/2015/7/3/1572163784851456/1572163790241792/STEM/c0a95e15d16643a2a69d6bd21d5d9265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da7f1da7e1c7aeaf845415de9aec0bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54218478418966f351be0d622a834f07.png)
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2016-12-03更新
|
203次组卷
|
2卷引用:2014-2015学年浙江省东阳中学高二下学期期中考试理科数学试卷
9 . 设函数
为自然对数的底数.
(I)当
时,函数
在点
处的切线为
,证明:除切点
外,函数
的图像恒在切线
的上方;
(II)当
时,设
是函数
图像上三个不同的点,求证:
是钝角三角形.
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663424352256/1572663430307840/STEM/ed7616e9869742c995ae61e6dbe53aab.png)
(I)当
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663424352256/1572663430307840/STEM/a596ecfd6e6442b0929710d03832864e.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663424352256/1572663430307840/STEM/ec6dbbc762c84aa0a356fb60a0c803d7.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663424352256/1572663430307840/STEM/799a5f024f4b4c968f07b8fd04be59e9.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663424352256/1572663430307840/STEM/c9a76dcd5fae4d5e9b61f124750b55c8.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663424352256/1572663430307840/STEM/799a5f024f4b4c968f07b8fd04be59e9.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663424352256/1572663430307840/STEM/ec6dbbc762c84aa0a356fb60a0c803d7.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663424352256/1572663430307840/STEM/c9a76dcd5fae4d5e9b61f124750b55c8.png)
(II)当
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663424352256/1572663430307840/STEM/640669c44a164f3186bad5aebf273116.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663424352256/1572663430307840/STEM/3a306a184aa74b829628055c4b8af2b4.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663424352256/1572663430307840/STEM/87c547d125ad4d6c8311da2965f5386d.png)
![](https://img.xkw.com/dksih/QBM/2016/5/31/1572663424352256/1572663430307840/STEM/cea054dbe1294d2f87e5ba91661bc1ad.png)
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2024高三·全国·专题练习
解题方法
10 . 已知函数
.
(1)当
时,求曲线
在
处的切线方程;
(2)若当
时,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63cf0b39c50f7b1de395431b02057251.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa4c355f11471a38f5583a434a1ddeb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d29c5c266a6d834a244c1f50c8f9848c.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5539cc3a6a9b1bda8013f0fd6760b4a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f5f7a36e251bbc424ccc127ebb2881.png)
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