1 . 水星是离太阳最近的行星,在地球上较难观测到.当地球和水星连线与地球和太阳连线的夹角达到最大时,称水星东(西)大距,这是观测水星的最佳时机(如图1).将行星的公转视为匀速圆周运动,则研究水星大距类似如下问题:在平面直角坐标系中,点A,
分别在以坐标原点
为圆心,半径分别为1,3的圆上沿逆时针方向做匀速圆周运动,角速度分别为
,
.当
达到最大时,称A位于
的“大距点”.如图2,初始时刻A位于
,
位于以
为始边的角
的终边上.
,当A第一次位于
的“大距点”时,A的坐标为______ ;
(2)在
内,A位于
的“大距点”的次数最多有______ 次
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3551176fd3003244122a34612d90113c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c896216c135b8c568a5f0987c23947e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22f9341d51c827a29a4a0b0b3dded16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7c7f579d5017888a314d681fe44db8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/590e165e407098fcac9f871beb047dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf01af951cc03381ca19150c6fe5364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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2 . 定义:给定函数
,若存在实数
、
,当
、
、
有意义时,
总成立,则称函数
具有“
性质”.
(1)判别函数
是否具有“
性质”,若是,写出
、
的值,若不是,说明理由;
(2)求证:函数
(
且
)不具有“
性质”;
(3)设定义域为
的奇函数
具有“
性质”,且当
时,
,若对
,函数
有5个零点,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63d7758a927384c13052ae432c20a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe17821ea81c6fec60bd5273901bd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ecb084837b614de935871d8f3dd2e1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c16d349946f1a9fbc12b28e7e9321c.png)
(1)判别函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d6e08526a91f8dfd160e7da2f92a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c16d349946f1a9fbc12b28e7e9321c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c16d349946f1a9fbc12b28e7e9321c.png)
(3)设定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae15be500f98d647a07fee39c95d041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eaae91ed6da60e86e3bb9b3eb7e03e60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ca276a67d4eca39a3c57dfab895e48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835eec12ec99561a3655c296570d75be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0db56c33be80c68078d92ba0ca47bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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名校
3 . 已知函数
定义域为
,满足
,且当
时,
,若对任意
,都
恒成立,则
的取值范围为()
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4811eeb79f8b96a551e31a000c21c43d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b14d0c440da20a2472608f1eec52eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ed2252a174be68cd6b1dbd878f445a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dee39c5a3e88d20afa8d372e187460d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc556b43885a04d45dfac05bf3bdd58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2020-03-02更新
|
774次组卷
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2卷引用:上海市上海中学2019-2020学年高一上学期期末数学试题
名校
4 . 已知函数
,给出下列四个判断:①函数
的值域是
;②函数
的图像时轴对称图形;③函数
的图像时中心对称图形;④方程
有实数解.其中正确的判断有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3318ee7c7c5e170bf253c70affcc2b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5432187d1c042787433b7633292d00fe.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/cb512cf73456084224bbcdd64d47f440.png)
A.1个 | B.2个 | C.3个 | D.4个 |
您最近一年使用:0次
2020-01-09更新
|
602次组卷
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4卷引用:上海市上海交通大学附属中学2021届高三上学期期末数学试题
上海市上海交通大学附属中学2021届高三上学期期末数学试题2018年上海市延安中学高考三模数学试题(已下线)1.1 命题及其关系基础练-2021-2022学年高二数学同步训练精选新题汇编(人教A版选修2-1)(已下线)第1章《直线与方程》 培优测试卷(一)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
5 . 已知函数
,且
在R上单调递增,且函数
与
的图象恰有两个不同的交点,则实数a的取值范围是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f6b58b6397c4ee44bf04209b39b89b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cc2e93cee2e6a921b66d250bd046b33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e204669efd2cd75f2bdee896d1cc1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e127daadf14bb6aaf557b717eb27ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11d71379442f28c038d367d49422cf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/987517758fad59f6f695761deb2a5ebd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2019-01-27更新
|
576次组卷
|
2卷引用:【市级联考】四川省宜宾市2018-2019学年高一秋季期教学质量监测数学试题
名校
6 . 定义:对于一个定义域为
的函数
,若存在两条距离为
的直线
和
,使得
时,恒有
,则称
在
内有一个宽度为
的通道.下列函数:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a35b5d5cdc099c96660349ca2f5c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e152ca40b53213d6bda22b6f03cd93a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1b531e92f4781302dd3d151bf13702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
①;②
;
③;④
.
其中有一个宽度为2的通道的函数的序号为
A.①② | B.②③ |
C.②④ | D.②③④ |
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2018-01-22更新
|
486次组卷
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2卷引用:【市级联考】辽宁省沈阳市2017-2018学年高一上学期期末数学试题