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1 . 已知函数
,有下列四个结论,其中正确的结论为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817aa2fdb7adb83e530e0a465b53a4c1.png)
A.![]() ![]() |
B.![]() ![]() |
C.当![]() ![]() ![]() |
D.![]() ![]() |
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2023-06-11更新
|
1586次组卷
|
4卷引用:辽宁省大连市第二十四中学2022-2023学年高一下学期期中数学试题
辽宁省大连市第二十四中学2022-2023学年高一下学期期中数学试题山东省日照市2022-2023学年高一下学期期末校际联合考试数学试题(已下线)第五章 三角函数(压轴题专练)-速记·巧练(人教A版2019必修第一册)(已下线)第五章 三角函数(32类知识归纳+38类题型突破)(6) -速记·巧练(人教A版2019必修第一册)
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2 . 已知函数
,其导函数为
,有以下两个命题:
①若
为偶函数,则
为奇函数;
②若
为周期函数,则
也为周期函数.
那么( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b79c4f1a0d03565b41758305edf1ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d31f9ce464f2ce3b24833b70595941c.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d31f9ce464f2ce3b24833b70595941c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d31f9ce464f2ce3b24833b70595941c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
那么( ).
A.①是真命题,②是假命题 | B.①是假命题,②是真命题 |
C.①、②都是真命题 | D.①、②都是假命题 |
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2023-04-13更新
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1036次组卷
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6卷引用:上海市文来中学2023-2024学年高二下学期期中考试数学试题
上海市文来中学2023-2024学年高二下学期期中考试数学试题上海市浦东新区2023届高三二模数学试题(已下线)专题03 导数及其应用上海市市北中学2024届高三上学期10月月考数学试题上海市闵行区七宝中学2024届高三下学期3月月考数学试题(已下线)专题05导数及其应用--高二期末考点大串讲(沪教版2020选修)
3 . 已知定义在R上的偶函数
满足
,
,若
,则不等式
的解集为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2504fdc8dc45e68e477760e43bc8124e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351950f5ef13f309b41dca7ac8e42300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ad022e083bb04aa44bb6cac10c0bed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5122b46fa16652aa887e5cce9b52eb23.png)
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2023-03-30更新
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1122次组卷
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7卷引用:四川省眉山冠城七中实验学校2022-2023学年高二下学期期中理科数学试题
名校
解题方法
4 . 已知函数
与
的定义域均为
,
分别为
的导函数,
,
,若
为奇函数,则下列等式一定成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348655470887ca720aa5a436867dda7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f8e496e36c3b89df188fd53140f3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5ac431c99c019d01f6aff1648e217f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2022-09-28更新
|
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8卷引用:湖南省邵阳市武冈市2022-2023学年高三上学期期中数学试题
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5 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/551b86489b6c4370026e0039644b5318.png)
A.函数![]() ![]() |
B.函数![]() |
C.直线![]() ![]() |
D.方程![]() |
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2022-05-23更新
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2155次组卷
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5卷引用:江西省宜春市宜丰县宜丰中学2022-2023学年高一上学期期中考试数学试题
江西省宜春市宜丰县宜丰中学2022-2023学年高一上学期期中考试数学试题江苏省常州市2022届高三下学期5月模拟数学试题河北省邯郸市魏县2022-2023学年高一上学期期末考试数学试题(已下线)必修第一册综合检测-人教A版(2019)必修第一册单元测试能力卷(已下线)第五章 三角函数(单元测试卷)-【同步题型讲义】(人教A版2019必修第一册)
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6 . 给定函数
、
,定义
为
、
的较小值函数.
(1)证明:
;
(2)若
,
,求
的最小正周期;
(3)若
,
,
,
,
,证明:
是周期函数的充要条件是
为有理数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c615e2f9c103b199ac959552462375ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf623a5466e1c865f2a0486de6c67bbc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34d910fb10ad65fcb6a65968232ad3e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ca6236721291138efa6ff93d5e1977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f422ae0c71734ed2f3e91fe831314e48.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d2ec20d9365a45443df03da489fa463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65b20cd5785f1a27979906b064363034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce21eee8b5a73aec951ab7b6712ab460.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8014b097bcc713cb46b0387b5465f17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd74add83d098d62539e2d8234e2d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cfcc567b95a320abcb25509923cd001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b287937887574e2c1e9a0222c3021936.png)
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解题方法
7 . 已知
是定义在
上的奇函数,且
,当
时,
关于函数
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b3b657ebd1733b4f19dcbec44919924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e46371f310e03a153a1698aad9d4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b24b654ecfaa92f61621b9303e8f91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d631520fc3505276dee02028f4c43d5.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
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2020-12-06更新
|
727次组卷
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6卷引用:山东省青岛市黄岛区2020-2021学年高三上学期期中考试数学试题
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8 . 设函数
、
的定义域均为
,若对任意
,且
,具有
,则称函数
为
上的单调非减函数,给出以下命题:① 若
关于点
和直线
(
)对称,则
为周期函数,且
是
的一个周期;② 若
是周期函数,且关于直线
对称,则
必关于无穷多条直线对称;③ 若
是单调非减函数,且关于无穷多个点中心对称,则
的图象是一条直线;④ 若
是单调非减函数,且关于无穷多条平行于
轴的直线对称,则
是常值函数;以上命题中,所有真命题的序号是_________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d200a7afe1e011713e14886a6887e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ba30f1aa5e75750c67b142fc1d7837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1f08e04cf0b6a9afea66ce590ba00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b334dafda377c3db77647c8cf1e95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c1dbaa1ddbcfe1cda0d6b7ea2068f19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06d499438273fcec25091823a6dc0be2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
名校
9 . 已知函数
,若定义在
上的奇函数
满足
,且
,则
=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558bb66c321aad244a877b4796412b20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0df5a071adc41863107f114be6400bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8d817224d09f763b265d435437a317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed2ad5b8845b50529adb20a083a7cf6a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2019-08-02更新
|
1942次组卷
|
3卷引用:江西省景德镇一中2019-2020学年高一上学期期中(1班)数学试题
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10 . 已知函数
是
上的偶函数,且满足
,在[0,5]上有且只有
,则
在[–2013,2013]上的零点个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7f0d29fad4807741d64b2e9f607b62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea10b79d5eba9f260d6a04bd2c7f9e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d479a86a1711709b2d100fe4daf3e7cf.png)
A.808 | B.806 | C.805 | D.804 |
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