名校
1 . 已知集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f912ee8b686b231b3e6ecbcf26250e.png)
(1)判断8,9,10是否属于集合
;
(2)已知集合
,证明:“
”的充分条件是“
”;但“
”不是“
”的必要条件:
(3)记集合
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f912ee8b686b231b3e6ecbcf26250e.png)
(1)判断8,9,10是否属于集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)已知集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/765038d98aaa2b44be5bc14b53baf76d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23af61cd402b3789af2401bde9cbefe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
(3)记集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74a5ab202f3250c69eb834f7399297f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0383768b4c98b3bc57d1abba6c381813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c458592ba2d5ddd559b8720438a8fe.png)
您最近一年使用:0次
2 . 回答下列问题
(1)已知
都是非零实数,且
,求证:
的充要条件是
.
(2)设
,且
,
,
,用反证法证明:
至少有一个大于0.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b21208364124b5c477b2ff8df1c2e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc539c71b72aff71e7c8e31e74969d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c328c9c4ec69c4275e27576fb61655.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b97ab3b66712c79b788f21ec005e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be4763ac99b71f7d741495e103f9eb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f658aef82183d509edd0078236b77b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7566946bb9631effbd92fa228477c550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
您最近一年使用:0次
名校
3 . (1)求证:已知
,
,
,
,
,并指出等号成立的条件;
(2)求证:对任意的
,关于
的两个方程
与
至少有一个方程有实数根(反证法证明);
(3)求证:使得不等式
对一切实数
,
,
都成立的充要条件是
,
,
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941b8c37cb9b036a5d7faa7eac01fa6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878f834c03d26711f64bb3abe20e5488.png)
(2)求证:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ace8f8a779c8f039407b7cae737d7212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751ee06608e9b40cd42cc4b48165e37c.png)
(3)求证:使得不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e774028355336f9a47e4e5194f3e7b06.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/e81e59019989b7dc2fb59b037ef6e010.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/fff8a8a07e9fab2efc5be33f1339112f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ad8d91c1ce139fbf2382a6e8a8f674.png)
您最近一年使用:0次
4 . (1)已知
是实数,集合
,
.求证:“
”是“
”的充要条件.
(2)设
.用反证法证明命题“若
,则
或
.”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8cc9571341dca622ca7b495f56af2cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49463959d426a3ad6931eb232e5e5e4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6606a5ae253107b4c200af0df215f64.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9e131cdd242d56b6dba05ab3363ef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eec336faee8689281a6f6b465e7fcff9.png)
您最近一年使用:0次
2020-11-13更新
|
247次组卷
|
3卷引用:上海市崇明区2020-2021学年高一上学期期中数学试题
名校
5 . (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)
您最近一年使用:0次
2020-10-27更新
|
459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
解题方法
6 . 已知函数
.
(1)若
满足
为R上奇函数且
为R上偶函数,求
的值;
(2)若函数
满足
对
恒成立,函数
,求证:函数
是周期函数,并写出
的一个正周期;
(3)对于函数
,
,若
对
恒成立,则称函数
是“广义周期函数”,
是其一个广义周期,若二次函数
的广义周期为
(
不恒成立),试利用广义周期函数定义证明:对任意的
,
,
成立的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17422461d5ec2bff93452619c6b774f3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b727eb9da56be079445321cf61cf26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be344d1925b25e44f3f8b34d2c193ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b186e49220460b09f85519aa657527b.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf03e1296f7f5bb315c87893caee079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4056806dc4a2f28e267f879b6f5c0079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c204be088a8fc6c096eedd5b1e7dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(3)对于函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06d64b48da95b74aa5e12bc5da127dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c90d0f5f17344c0eb75c2aea394bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2183ba00d69af06d9a950469b38cfe4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a35277c37144276ead40bb74a51481.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2183ba00d69af06d9a950469b38cfe4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb05fd7662d05b9e2051b044de722840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd423a80d5b6fea8753fa1813cfbcc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859458471c86ae39e0cc42d2d960d03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f05dd02b6f561dcf94bab8a3160108d5.png)
您最近一年使用:0次
2020-08-25更新
|
1051次组卷
|
6卷引用:3.2函数的基本性质-2020-2021学年高一数学同步课堂帮帮帮(人教A版2019必修第一册)
(已下线)3.2函数的基本性质-2020-2021学年高一数学同步课堂帮帮帮(人教A版2019必修第一册)2019年上海市建平中学高三三模数学试题(已下线)专题2.3 函数的奇偶性与周期性(精讲)-2021年高考数学(理)一轮复习学与练(已下线)专题2.3 函数的奇偶性与周期性(精讲)-2021届高考数学(理)一轮复习讲练测上海市建平中学2019届高三下学期5月月考数学试题(已下线)专题03 函数的概念与性质(模拟练)-2
20-21高一上·全国·课后作业
7 . 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
名校
8 . 对于定义在
上的函数
,若存在实数
及
、
(
)使得对于任意
都有
成立,则称函数
是带状函数;若
存在最小值
,则称
为带宽.
(1)判断函数
是不是带状函数?如果是,指出带宽(不用证明);如果不是,请说明理由;
(2)求证:函数
(
)是带状函数;
(3)求证:函数
是带状函数的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7eda9b9aed5fd932841a7d5dab7a214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e762379a924f4574e938b352ea0fc809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45aec1e4ca31a14444f4bc8682ab5d9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f300447fb05def5f74d0679fc6ea881.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da51ba51157f2b7953f66a3eaaf20e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
(3)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/152fc8ec17c4a0b3a059d0a87c4160bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd9cdea1e995c59e5d3225acad8b4d3c.png)
您最近一年使用:0次
名校
9 . 给出集合![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0c0d57080c83dfae371038b34fbc57.png)
(1)若
求证:函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d4f7bcbafb423271f97e0d407c74ec.png)
(2)由(1)可知,
是周期函数且是奇函数,于是张三同学得出两个命题:
命题甲:集合M中的元素都是周期函数;命题乙:集合M中的元素都是奇函数,请对此给出判断,如果正确,请证明;如果不正确,请举出反例;
(3)设
为常数,且
求
的充要条件并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d0c0d57080c83dfae371038b34fbc57.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca64afa00211df204a6302463890edbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d4f7bcbafb423271f97e0d407c74ec.png)
(2)由(1)可知,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d95da33526f7713ce2016bfa6efe0f.png)
命题甲:集合M中的元素都是周期函数;命题乙:集合M中的元素都是奇函数,请对此给出判断,如果正确,请证明;如果不正确,请举出反例;
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c99ac91fc1e9097126e4c2aa20cdeffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc1d1fd01b97f1f5414428bc0d711d0.png)
您最近一年使用:0次
10 . 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)
您最近一年使用:0次
2019-09-19更新
|
467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