名校
解题方法
1 . 已知函数
.若存在
,对于任意的
,
,则a的一个取值可以是______ ;满足条件的a值共有______ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8afc17028d1394d4520540aaea9f85a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51159984b2cb00f30b3986315019623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533399d365ace8a627f7c81d10d83a53.png)
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名校
解题方法
2 . 高斯是德国著名数学家,近代数学奠基者之一,享有“数学王子”称号,他和阿基米德、牛顿并列为世界三大数学家,用其名字命名的“高斯函数”为:设
,用
表示不超过
的最大整数,则
称为高斯函数,例如
,
. 已知函数
,函数
,则下列4个命题中,其中正确结论的选项是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1dffa925101e9e19720ee7295133d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be209b4634a4169d727f9fac198acce3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bbc6c3245906550c7641ce0471ac202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c583c96c958b9653dd9b66f7dbd7079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da9bcf0effd771e30ab3399d2fcd9fdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0bed8d403d5e4e232c8ac65ed87af5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259118296ced0cf932f15d08c3feee77.png)
A.函数 ![]() |
B.函数 ![]() ![]() |
C.函数 ![]() ![]() |
D.方程 ![]() |
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3 . 太极图是由黑白两个鱼形纹组成的图案,俗称阴阳鱼,太极图展现了一种互相转化,相对统一的和谐美.定义:能够将圆
的周长和面积同时等分成两个部分的函数称为圆
的一个“太极函数”.则下列有关说法中:①对于圆
的所有非常数函数的太极函数中,一定不能为偶函数;②函数
是圆![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/07f5f0c5ff574d97acda5ccde08c7ab9.png?resizew=23)
的一个太极函数;③存在圆O,使得
是圆O的一个太极函数; ④直线
所对应的函数一定是圆![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/07f5f0c5ff574d97acda5ccde08c7ab9.png?resizew=23)
的太极函数;⑤若函数
是圆
的太极函数,则
.所有正确的是___________ .
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/d46ff1964164482f92a174b097e85c9e.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/d46ff1964164482f92a174b097e85c9e.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/09d13ca1b7584f29bf879f96d2f032fa.png?resizew=97)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/22b62c75c58e4533a94d06423566b5be.png?resizew=103)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/07f5f0c5ff574d97acda5ccde08c7ab9.png?resizew=23)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/e8f745b46dba4e3f9e6cb157011647ad.png?resizew=107)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/7a159f969dc74d9c8d16a2e64f22a1d2.png?resizew=91)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/342fbc44ef374d3a921bf28a320dfe3b.png?resizew=177)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/07f5f0c5ff574d97acda5ccde08c7ab9.png?resizew=23)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/05a746b7fcc24f748eef5a8a71fd784b.png?resizew=201)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/791ed4ad68564e89b37d27e644f7ae01.png?resizew=151)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/09d13ca1b7584f29bf879f96d2f032fa.png?resizew=97)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/3f20ee04df6b435a90a349854f42c422.png?resizew=69)
![](https://img.xkw.com/dksih/QBM/2016/7/15/1572922760560640/1572922766753792/STEM/715580bf-2b1a-459c-a2c7-5f8fecd84cd2.png?resizew=161)
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2016-12-04更新
|
286次组卷
|
2卷引用:2016届四川省树德中学6月高考适应性测试理科数学试卷
2014·上海·二模
名校
4 . 对于函数
,若存在区间
,使得
,则称函数
为“可等域函数”,区间
为函数
的一个“可等域区间”.给出下列4个函数:
①
;②
; ③
; ④
.
其中存在唯一“可等域区间”的“可等域函数”为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4728362b29de88a7a9b5b5d3bf6d894.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd1ca0cf68bef34f39b9701f0b56205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f94a72c1a0c2801efe9f3bb1a412c21a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1439c562a1331c7245f7ad4c70e0b6b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de73a16db57317970e8da776b78af9ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda824b37b5420579555fdacece101ec.png)
其中存在唯一“可等域区间”的“可等域函数”为( )
A.①②③ | B.②③ | C.①③ | D.②③④ |
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2014-04-24更新
|
2237次组卷
|
8卷引用:2014届上海市六校高三下学期第二次联考理科数学试卷