1 . 以
间的整数
为分子,以
为分母组成分数集合
,其所有元素和为
;以
间的整数
为分子,以
为分母组成不属于集合
的分数集合
,其所有元素和为
;……,依次类推以
间的整数
为分子,以
为分母组成不属于
的分数集合
,其所有元素和为
;则
=________.
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/b53c9837b44642baa75ff3707709cb0d.png?resizew=40)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/ee6269083ca3498386f0f921a53cf592.png?resizew=95)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/719fe1d4856e4e069a5b5741ac6e5af6.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/22d592c9cbae4e4bbb7f205a0e40ff40.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/d1675699c2a446519e5cd124bfb0a097.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/96f31b7449074a10bf4b00960a6028b3.png?resizew=47)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/ee6269083ca3498386f0f921a53cf592.png?resizew=95)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/3989c5afb9764fa2864a78e4d8076bc1.png?resizew=23)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/22d592c9cbae4e4bbb7f205a0e40ff40.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/ac344738f78445a799262d40ed14d1c6.png?resizew=20)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/eec772b58d6d4168b40a74292ff75534.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/8ab2ae2657554b11be6f1d32c9f28e9b.png?resizew=47)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/ee6269083ca3498386f0f921a53cf592.png?resizew=95)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/7210aeb22bbb4373819609eff9728d27.png?resizew=23)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3e7202eaa223ad048b1fda5180d0ca.png)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/d00747e7035e409ca56129a2b1f0ec07.png?resizew=20)
![](https://img.xkw.com/dksih/QBM/2014/4/28/1571688545214464/1571688550998016/STEM/49ee7babdc9649f98473ca8728bceb46.png?resizew=19)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fe8fecffe2d718a9a346173e5f7e6e.png)
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2 . 设
是定义在
上的函数,若对任何实数
以及
中的任意两数
、
,恒有
,则称
为定义在
上的
函数.
(1)证明函数
是定义域上的
函数;
(2)判断函数
是否为定义域上的
函数,请说明理由;
(3)若
是定义域为
的函数,且最小正周期为
,试证明
不是
上的
函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034e4d52bd5ae47074a93c0647f67399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/297ea61edb0df90702a637c110c24d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24464329963c0fff6738eb9f57da0723.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e0c9333f46def8beef5a9ed59ff4bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)若
![](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/0b68df477b3ee45ac0f725db00d465a1.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/c5db41a1f31d6baee7c69990811edb9f.png)
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2016-12-03更新
|
1042次组卷
|
3卷引用:2015届上海市奉贤区高三上学期期末调研测试数学试卷
12-13高一下·江苏扬州·阶段练习
名校
3 . 定义区间
的长度均为
,其中
.已知实数
,则满足
的
构成的区间的长度之和为 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36051bfe736319addd75dbad8363ace4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08d9560a5a060961e957ffeff10a29aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ecebb31ea8ee6db240b42a5ee2c5e88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa0653197cd4a5e31febc2173404ce2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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2019-01-30更新
|
501次组卷
|
3卷引用:上海市奉贤中学2017-2018学年高一上学期10月月考数学试题
名校
4 . 已知
,数列
满足
,对于任意
都满足
,且
,若
,则
的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54664b7be0f083657f3446429e2802a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ea8d0e50065114b05ef2dc1ea1129cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d3ed172955c49c2b52923c47fc5948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f775de74d74ba9d2e6b26888cfa3847d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d83f1b80fe514c52a3d06ea814fc7d5.png)
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2017-12-25更新
|
404次组卷
|
3卷引用:上海市奉城高级中学2019届高三上学期10月月考数学试题
5 . 对于正项数列
,若
对一切
恒成立,则
对
也恒成立是真命题.
(1)若
,
,且
,求证:数列
前
项和
;
(2)若
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50ce3e0fbf5a125d7d4622bbe7a5e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f009319db5b51c8f5d3a12d4e2119b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9645bd4d2002993b90ec6d48f9c04f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f594a129c9108ccd0292f7009718550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f4cba97e970f98d7e2c5f62d4299c3f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4223bd6ee8f82d59d244371fbcddc5.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572057013944320/1572057020022784/STEM/050687f2755147f5bf8284ed60e44c11.png?resizew=192)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72729d795c2cf94ebecc257813db8755.png)
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11-12高三·上海奉贤·期末
6 . 函数
,定义f(x)的第k阶阶梯函数
,其中k∈N*,f(x)的各阶梯函数图象的最高点Pk(ak,bk),最低点Qk(ck,dk).
(1)直接写出不等式f(x)≤x的解;
(2)求证:所有的点Pk在某条直线L上.
(3)求证:点Qk到(2)中的直线L的距离是一个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647103b243eb9c05762f7e6ef0649449.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9dc44ba2a4f5f09f3c5e77b1975ad54.png)
(1)直接写出不等式f(x)≤x的解;
(2)求证:所有的点Pk在某条直线L上.
(3)求证:点Qk到(2)中的直线L的距离是一个定值.
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11-12高三·上海奉贤·期末
7 . 出租车几何学是由十九世纪的赫尔曼-闵可夫斯基所创立的.在出租车几何学中,点还是形如
的有序实数对,直线还是满足
的所有
组成的图形,角度大小的定义也和原来一样.直角坐标系内任意两点
定义它们之间的一种“距离”:
,请解决以下问题: (1)求点
、
的“距离”
;
(2)求线段
上一点
的距离到原点
的“距离”;
(3)定义:“圆”是所有到定点“距离”为定值的点组成的图形,点
求经过这三个点确定的一个“圆”的方程,并画出大致图象;(说明所给图形小正方形的单位是1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42dfb56b5bcb3c3954d7d65cc12fea49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae35beffd38dfb117b57804a9042b886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42dfb56b5bcb3c3954d7d65cc12fea49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba69c334a66df7f45e382c1528c94ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba1f5820426a563fede050649122d945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca979687ffb2214e747525635a6912c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b80ac9ca466eb94c7e0354f9cacb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80cb4d2d461646bf1d49ec66f3304ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686be4dc7a016d6f67f9043960e46b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93c7781652e183fefe7b0b8578da2735.png)
(3)定义:“圆”是所有到定点“距离”为定值的点组成的图形,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187ddb68acf4efce9542d72cf5bd491f.png)
![](https://img.xkw.com/dksih/QBM/2012/1/28/1570701930340352/1570701935984640/STEM/e564d3079d0e4d96b17a82d5a842615a.png?resizew=334)
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11-12高三·上海奉贤·期末
8 . 正数列
的前n项和
满足:r
,
常数r∈N.
(1)求证:an+2﹣an是一个定值;
(2)若数列{an}是一个周期数列,求该数列的周期;
(3)若数列{an}是一个有理数等差数列,求Sn.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe229b24e2d56ff6b491725ceae4ff2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b708c8dcb2d66eb2ce0b3718a9cd924a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04915f8cfc4bec87e92a9f25bab42f69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae9e5903128c8e5fd29de1389a8a3941.png)
(1)求证:an+2﹣an是一个定值;
(2)若数列{an}是一个周期数列,求该数列的周期;
(3)若数列{an}是一个有理数等差数列,求Sn.
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解题方法
9 . 已知平面向量
,
,
,
满足:
,
,
,
,则
的最大值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b76118bdca6c463cfb19b66f30281c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e49ef047ee5a1b9a88442b038b18f995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17178a2c22a5d3f3d6a7948c58377ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8e7def6dcf30452017593c880ca6c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329aaa56f21c61f43c60ee84316be091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbd3ac3917ceabdb633e2a2e66c4a015.png)
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