名校
解题方法
1 . 对任意的非空数集
,定义:
,其中
表示非空数集
中所有元素的乘积,特别地,如果
,规定
.
(1)若
,请直接写出集合
和
中元素的个数.
(2)若
,其中
是正整数
,求集合
中元素个数的最大值和最小值,并说明理由.
(3)若
,其中
是正实数
,求集合
中元素个数的最小值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7334e66713c1bb166178d5250f85bce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c363cfd3ada27d5756b6f6512f4b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfc0853aa05ca4ea6a80b7db3a9f702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2dd216be69d8aa90c1a09d67f15374d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e88ec106805854932acac7773085e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29b2c411cea591bb0352687b73fa1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9cad3d008dc3dc18be02b702f7937ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0616b5ffd9092ac782e5bb529482a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56729bd5cfde71dd6d04780792a70b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376e5582c1942682ee5ddb3831d09610.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaae479eb6c8af3d600ae81dbf91fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c5330613e7a260dee6b7914ccd0d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/376e5582c1942682ee5ddb3831d09610.png)
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2023-06-14更新
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384次组卷
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3卷引用:四川省南充市顺庆区南充高级中学2023-2024学年高一上学期10月月考数学试题