名校
解题方法
1 . 某地计划在水库建一座至多安装3台发电机的水电站.过去50年的水文资料显示,水库年入流量
(年入流量:一年内上游来水与库区降水之和.单位:亿立方米)都在40以上,其中,不足80的年份有10年,不低于80且不超过120的年份有35年,超过120的年份有5年,将年入流量在以上三段的频率作为相应段的概率,并假设各年的年入流量相互独立.
(1)求未来4年中,至多有1年的年入流量超过120的概率;
(2)水电站希望安装的发电机尽可能运行,但每年发电机最多可运行台数受年入流量
限制,并有如下关系:
若某台发电机运行,则该台发电机年净利润为5000万元;若某台发电机未运行,则该台发电机年维护费与年入流量
有如下关系:
欲使水电站年净利润最大,应安装发电机多少台?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)求未来4年中,至多有1年的年入流量超过120的概率;
(2)水电站希望安装的发电机尽可能运行,但每年发电机最多可运行台数受年入流量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
年入流量 | |||
发电机最多可运行台数 | 1 | 2 | 3 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
年入流量 | ||
一台未运行发电机年维护费 | 500 | 800 |
您最近一年使用:0次
2020-05-15更新
|
1082次组卷
|
3卷引用:2020届山东省淄博市高三10月摸底考试数学试题
2 . 两个数列
、
,当
和
同时在
时取得相同的最大值,我们称
与
具有性质
,其中
.
(1)设
的二项展开式中
的系数为
(
),
,记
,
,
,依次下去,
,组成的数列是
;同样地,
的二项展开式中
的系数为
(
),
,记
,
,
,依次下去,
,组成的数列是
;判别
与
是否具有性质
,请说明理由;
(2)数列
的前
项和是
,数列
的前
项和是
,若
与
具有性质
,
,则这样的数列
一共有多少个?请说明理由;
(3)两个有限项数列
与
满足
,
,且
,是否存在实数
,使得
与
具有性质
,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7728d33987f271f5ec625592076593b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d032d57e0d95dddb3d4501249f1327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7728d33987f271f5ec625592076593b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d032d57e0d95dddb3d4501249f1327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ca4f2b82d9d7a8323c8d697338a6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7728d33987f271f5ec625592076593b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d032d57e0d95dddb3d4501249f1327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5839a256b56cb644d8a76fa40da0f339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce733aaa0bf65084fedbf529da36ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e668f6e2cbdb731bac88892e47fddf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e10f2f74e201f77f853e9ed9078615c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8140a39887c6b0b3f26b226c090a3127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78908ea2f65b1af56be13743cf5c3faf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf87d2d47a420aee5be760a6de0d3bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a28198a932f4f9a93a4c613bbc2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce733aaa0bf65084fedbf529da36ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e668f6e2cbdb731bac88892e47fddf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e10f2f74e201f77f853e9ed9078615c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f0f8b318bae5924c4d2b0194946f259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d54d77d1248bbd1398a828a3389ce78f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ba468c3d2d7b3fa8e65885bfacf4a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ef4c4439b36c2847b0056a116d56d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21ab17f8694a07cfcc9e63389b34690.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d5d0896cc32b7f445c3dab320482515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce224c28ca451c4f105dc3b077736cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eded65284816fdf6bf335b0c2a78e6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a81decee0ccfa372af8951ca73ada38a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d21ab17f8694a07cfcc9e63389b34690.png)
(3)两个有限项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/043d21c4badb8e2bd98390c7f1c25822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10b3cf64372426d1d2faff63d34fdcd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
解题方法
3 . 规定:对于任意实数
,若存在数列
和实数
,使
,则称
可以表示成
进制形式,简记为:
;如:
,表示
是一个2进制形式的数,且
;
(1)已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dff740b3b15a876e6de4e1a2783bcdf.png)
,试将
表示成
进制的简记形式;
(2)若数列
满足
,
,
,
,
,求证:
;
(3)若常数
满足
且
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db02c520989da5adce55d84410a644b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c5827acadcb93523ae7fa25204ebcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49fb140af76ff062c908e96e9dab466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69946ed268a024eca1cf522acee6985a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0328bf462207065c2e0eaaba1002ef1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dff740b3b15a876e6de4e1a2783bcdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aebf62d230cbee1781de6c1d73a7ff6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7f1ce82982b8385d78e8e77c8f1e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b6d151d3f864bae873987f6db9327a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb701fb5c95b3612e64712d836754860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed6ef8ef7af86ebdca4f34a36989a63.png)
(3)若常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e12b644318c5c276a086a82982b8dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e909ffa98363a211839d0b1338afbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137510e8bcf483cdb40a0592140a800a.png)
您最近一年使用:0次
名校
4 . 对于数列
,称
(其中
)为数列
的前k项“波动均值”.若对任意的
,都有
,则称数列
为“趋稳数列”.
(1)若数列1,
,2为“趋稳数列”,求
的取值范围;
(2)已知等差数列
的公差为
,且
,其前
项和记为
,试计算:
(
);
(3)若各项均为正数的等比数列
的公比
,求证:
是“趋稳数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98816fb04cd9855c376352b915c41b42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6aaee5e84eb6c6a4f339fe82c20025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6aaee5e84eb6c6a4f339fe82c20025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca48e93a553f5828b86e09f4d5f1042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
(1)若数列1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)已知等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/370c1c8c958a7010fa144eb32e23f8d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f0bf06a83e595c7195e5c3cfd53a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea88016f672b8f54901e457cceecca1.png)
(3)若各项均为正数的等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fecd48d65ac4f8197c45231f68e8bce1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
您最近一年使用:0次
2020-02-01更新
|
1847次组卷
|
5卷引用:2016届上海市松江区高三上学期期末质量监控(文)数学试题
5 . 已知函数
.
(1)指出
的单调区间;(不要求证明)
(2)若
满足
,且
,求证:
;
(3)证明:当
时,不等式
对任意
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e36e6158c7da6ebbf95da58658a998.png)
(1)指出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad5124201a1776222070104ceb306c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804c5ac86fac689aa1102df1cefafc7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a68f76d4feecadef02aa09a084f75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd69d26f76d5a55cf072fa49b53d437.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48adb8a59b5c02fad5eada1b35171cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b7667435fbb850e751297135b5725a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d6f67a296f5790649068d2441d5bb98.png)
您最近一年使用:0次