名校
1 . 高斯函数
是用德国著名的数学家高斯的名字命名的,即设
,用
表示不超过
的最大整数,例如
,
.已知函数
,有下列四个结论:①
;②
在
上单调递增;③
的最小值为0;④
没有最大值,其中所有正确结论的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7179c645736d68c90023f83d7f11ed01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985227b7b4703f3ed8717d0abc4febfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec13b2c5950301683e240faf02340617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e86444c5514b63b441f29c0f511750a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/956cd0c33242381c2f977ab7b0435448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad2edd8edcb21bd41584daf9bb95a5c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
A.①②③ | B.①③④ | C.①④ | D.①② |
您最近一年使用:0次
2024-04-08更新
|
191次组卷
|
2卷引用:山西省大同市第二中学校2023-2024学年高一下学期3月月考数学试题
2 . 两个数互素是指两个正整数之间除了1之外没有其他公约数.欧拉函数
(
)的函数值等于所有不超过正整数n,且与n互素的正整数的个数,例如
,
.
关于欧拉函数给出下面四个结论:
①
;
②
,恒有
;
③若m,n(
)都是素数,则
;
④若
(
),其中
为素数,则
.
(注:素数是指除了1和它本身以外不再有其他因数,且大于1的正整数.)
则所有正确结论的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc89a53c03cb86fb653bb82128f6cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9edd29e22f6a7f4d14d9f8d2684d47e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39de1bc04496b97dcf401c669e6ab44e.png)
关于欧拉函数给出下面四个结论:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bb88141edd6ddf3efbede1cb9b9051.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71b78297a65e7fad69635b19928ecc10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2eb229ae25851eae3cf941fd46eca4.png)
③若m,n(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d9712c3b25f3030e166e136d3a4686.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8178596507fe45cea77096a53d6395.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13ae00da0e4adace07489880ab64d391.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ef0a61e3c701a7cb3a9f9ca3c8dd37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bced1fbb4e3bde1437f4fb2821d81a9.png)
(注:素数是指除了1和它本身以外不再有其他因数,且大于1的正整数.)
则所有正确结论的序号为
您最近一年使用:0次
名校
解题方法
3 . 已知定义在
上的偶函数
满足:
,且当
时,
单调递减,给出以下四个命题:
①
;
②
为函数
图象的一条对称轴;
③ 函数
在
单调递增;
④ 若方程
在
上的两根为
,
,则
.
上述命题中所有正确命题的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feedd7224f069d6d4796a3b6e5b23e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec65a2bec3d4296c613a80b3ae41d5e.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
③ 函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71913ad3245e04f709e91a68553f8a75.png)
④ 若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c0d827ef8598ba6b70b34b2bdcd1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9eb53c0560847e76d648116f8bc4de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbdd93875258193ea4d7dfbd5270f06e.png)
上述命题中所有正确命题的序号为
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解题方法
4 . 下列说法中:
①满足
的实数x的取值范围为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5322996312b017b1cbcddd57c716e9.png)
②
表示
与
中的较小者,则函数
的最大值为1;
③若函数
的单调递增区间是
,则
;
④已知
的定义域为
,且满足对任意
,有
,则
为偶函数.
其中正确说法的序号是_______ 注:把你认为是正确的序号都填上).
①满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15ac7c1583055847ccda17ea020033f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5322996312b017b1cbcddd57c716e9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7987d79822aed7c0b8760256722fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/733c28f914c50ff3b5b26237e70643a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
③若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ffac4ed594636b076cb4cc9e18f102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a9e66b73038b6279d204a47a78902ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7300838ad476bc1c75c1cca1fc9880cf.png)
④已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5259b38698a36da71ca43521fe18615e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc1bc250c8a6523a1be394ff48d4a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23478a1fcd7ba7a2a7adc61f20b1d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
其中正确说法的序号是
您最近一年使用:0次