1 . 已知①设函数
的值域是
,对于
中的每个
,若函数
在每一处
都等于它对应的
,这样的函数
叫做函数
的反函数,记作
,我们习惯记自变量为
,因此
可改成
即为原函数的反函数.易知
与
互为反函数,且
.如
的反函数是
可改写成
即为
的反函数,
与
互为反函数.②
是定义在
且取值于
的一个函数,定义![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6c5d65e0ccd27748fcbc420c6a2e22.png)
,则称
是函数
在
上的
次迭代.例如
,则
.对于一些相对复杂的函数,为求出其
次迭代函数,我们引入如下一种关系:对于给定的函数
和
,若函数
的反函数
存在,且有
,称
与
关于
相似,记作
,其中
称为桥函数,桥函数满足以下性质:
(i)若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0e8a92152787274ed6e06a21ef1661.png)
(ii)若
为
的一个不动点,即
,则
为
的一个不动点.
(1)若函数
,求
(写出结果即可)
(2)证明:若
,则
.
(3)若函数
,求
(桥函数可选取
),若
,试选取恰当桥函数,计算
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e66c24e657d998beb013ad1fb311d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f93e3581e920716e710e22b31006bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f93e3581e920716e710e22b31006bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63ced31d098cfb0cf14d906e97e6353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e66c24e657d998beb013ad1fb311d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955f3c2b80eebc3f88c804112e5f41f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955f3c2b80eebc3f88c804112e5f41f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb87ce86e2c9a1a8188b03b74438fdd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb87ce86e2c9a1a8188b03b74438fdd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e66c24e657d998beb013ad1fb311d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ef38135b0e7906687d8a4918a4cb67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43737e3ca063dfc210d0c72924a4930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808bd2fc4b344e7669fca65b4fa122df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808bd2fc4b344e7669fca65b4fa122df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6c5d65e0ccd27748fcbc420c6a2e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c110a1293773729278a214c7fe8d544e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33cfe27fd2276a7c542f062c17b4d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/052ddf3664af9ab2990f3ea622997e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910ca4e4f009554b599eab90e1d94c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71567deb76e48f8a2424b06536cbe465.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66b033ee7a03c7b3508583481465275.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1249f186df944244da02e1b8c754005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
(i)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1249f186df944244da02e1b8c754005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0e8a92152787274ed6e06a21ef1661.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f199ad3fad8657afa38f370b319a75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192bb45bd15b200f40b34377bc58905b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33cfe27fd2276a7c542f062c17b4d85.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1249f186df944244da02e1b8c754005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99315f5b2ae9bea18e06401b41d3780c.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/becd598a11b876d858728161a7a09705.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33cfe27fd2276a7c542f062c17b4d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ab7717944da2b6cc305b6a65f91408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85f9d9be0ba965ff7beb0e011267f29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bee7f1ccd52c7d526b6d466b970e769.png)
您最近一年使用:0次
名校
2 . 火电厂、核电站的循环水自然通风冷却塔是一种大型薄壳型构筑物.建在水源不十分充足的地区的电厂,为了节约用水,需建造一个循环冷却水系统,以使得冷却器中排出的热水在其中冷却后可重复使用,大型电厂采用的冷却构筑物多为双曲线型冷却塔.此类冷却塔多用于内陆缺水电站,其高度一般为75~150米,底边直径65~120米. 双曲线型冷却塔比水池式冷却构筑物占地面积小,布置紧凑,水量损失小,且冷却效果不受风力影响;它比机力通风冷却塔维护简便,节约电能;但体形高大,施工复杂,造价较高.(以上知识来自百度,下面题设条件只是为了适合高中知识水平,其中不符合实际处请忽略.)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/c7842de3-87fa-47f5-ade5-71fb0145e144.png?resizew=107)
(1)如图为一座高100米的双曲线冷却塔外壳的简化三视图(忽略壁厚),其底面直径大于上底直径,已知其外壳主视图与左视图中的曲线均为双曲线,高度为100
,俯视图为三个同心圆,其半径分别40
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb950416953a22cbd20182188b0cd4c.png)
,30
,试根据上述尺寸计算视图中该双曲线的标准方程(
为长度单位米);
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/39573f23-d44a-430b-9398-a896b202b94f.png?resizew=161)
(2)试利用课本中推导球体积的方法,利用圆柱和一个倒放的圆锥,计算封闭曲线:
,
,绕
轴旋转形成的旋转体的体积多少?(用
表示).(用积分计算不得分)现已知双曲线冷却塔是一个薄壳结构,为计算方便设其内壁所在曲线也为双曲线,其壁最厚为0.4
(底部),最薄处厚度为0.3
(喉部,即左右顶点处),试计算该冷却塔内壳所在的双曲线标准方程是?并计算本题中的双曲线冷却塔的建筑体积(内外壳之间)大约是多少
;(计算时
取3.14159,保留到个位即可)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/4f3b4732-84ed-4c2a-948d-24d17a7688bc.png?resizew=251)
(3)冷却塔体型巨大,造价相应高昂,本题只考虑地面以上部分的施工费用(建筑人工和辅助机械)的计算,钢筋土石等建筑材料费用和和其它设备等施工费用不在本题计算范围内.超高建筑的施工(含人工辅助机械等)费用随着高度的增加而增加,现已知:距离地面高度30米(含30米)内的建筑,每立方米的施工费用平均为:400元/立方米;30米到40米(含40米)每立方米的施工费用为800元/立方米;40米以上,平均高度每增加1米,每立方米的施工费用增加100元.试计算建造本题中冷却塔的施工费用(精确到万元).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/c7842de3-87fa-47f5-ade5-71fb0145e144.png?resizew=107)
(1)如图为一座高100米的双曲线冷却塔外壳的简化三视图(忽略壁厚),其底面直径大于上底直径,已知其外壳主视图与左视图中的曲线均为双曲线,高度为100
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eb950416953a22cbd20182188b0cd4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/39573f23-d44a-430b-9398-a896b202b94f.png?resizew=161)
(2)试利用课本中推导球体积的方法,利用圆柱和一个倒放的圆锥,计算封闭曲线:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b930a9ba90cdd9e62d8a3892125825c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e51aff9ae2fa123ae63f19478db507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36accab23dbd172687769aea43e5781c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/4f3b4732-84ed-4c2a-948d-24d17a7688bc.png?resizew=251)
(3)冷却塔体型巨大,造价相应高昂,本题只考虑地面以上部分的施工费用(建筑人工和辅助机械)的计算,钢筋土石等建筑材料费用和和其它设备等施工费用不在本题计算范围内.超高建筑的施工(含人工辅助机械等)费用随着高度的增加而增加,现已知:距离地面高度30米(含30米)内的建筑,每立方米的施工费用平均为:400元/立方米;30米到40米(含40米)每立方米的施工费用为800元/立方米;40米以上,平均高度每增加1米,每立方米的施工费用增加100元.试计算建造本题中冷却塔的施工费用(精确到万元).
您最近一年使用:0次
2019-09-23更新
|
680次组卷
|
2卷引用:上海市宝山区交大附中2018-2019学年高二下学期期中数学试题
3 . 设12元实数集合
满足:可将其划分为两个6元子集
和
,使得对每个
,均有
,则这样的
可以是______ .(写出一个即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab68ee11734bd89733c3064af16cea50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe342a96adffebbb5d59c5fcfd138e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fde1b1e2b446a4db8650c9fdab83766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff197132463fd76db478b76ed2cf653c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/908fbdc652b3cafc1f4d0b2e3ae2a094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
解题方法
4 . 数列
中,给定正整数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
,
.定义:数列
满足
,称数列
的前
项单调不增.
(Ⅰ)若数列
通项公式为:
,求
;
(Ⅱ)若数列
满足:
,求证
的充分必要条件是数列
的前
项单调不增;
(Ⅲ)给定正整数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
,若数列
满足:
,且数列
的前
项和为
,求
的最大值与最小值.(写出答案即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad58ed5a48295f7f18a5225ba8d587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9560ef128e41e22e920cad05478703a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a1a71b07e029a192496616fb7b51ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(Ⅰ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c8b1004db0d954d20c6254a7308847f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675123cce20a9ce670fb7ae18943bde7.png)
(Ⅱ)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f28ba33c7d7fe2730f4ac058ac2f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a2be1c992655c9c3aa49804d2eb4d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(Ⅲ)给定正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad58ed5a48295f7f18a5225ba8d587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198955f27e060b6628f703d0b4d278a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d7b4bb12628d5ed455d814b8aafa1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8861a2221f16a11415179361c7058a.png)
您最近一年使用:0次
5 . 对于数列A:
,经过变换T:交换A中某相邻两段的位置(数列A中的一项或连续的几项称为一段),得到数列
.例如,数列A:
经交换M,N两段位置,变换为数列
:
.设
是有穷数列,令
.
(1)如果数列
为3,2,1,且
为1,2,3.写出数列
;(写出一个即可)
(2)如果数列
为9,8,7,6,5,4,3,2,1,
为5,4,9,8,7,6,3,2,1,
为5,6,3,4,9,8,7,2,1,
为1,2,3,4,5,6,7,8,9.写出数列
;(写出一组即可)
(3)如果数列
为等差数列:2015,2014,…,1,
为等差数列:1,2,…,2015,求n的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304e71a623c4412188a800046a970d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc250de2317c83a904f0ebce5fc2989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bbf1fc7753df7951558e56b71b78c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc250de2317c83a904f0ebce5fc2989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a403f562ca2b40d07069aace053e8af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a60554299801b8c94f80e04398e589.png)
(1)如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
(2)如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfefd19874aeff8340735b3df468333.png)
(3)如果数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7356ec98b600ece41f3a6b4bc26a7d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
您最近一年使用:0次
6 . 设双曲线Γ:
,
,B,C在Γ上且直线
经过A.设
分别为Γ在B,C处的切线,点D满足
,则D的轨迹方程是___________ ;若D的横纵坐标均为正整数,且二者之和大于2024,则D可以是_____ .(写出1个即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3674d64026a371b001453280477ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86de0e038b0304e34ca8c9b117fec917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04e6aa92080d4e1f43a1ac2f9c2965fe.png)
您最近一年使用:0次
名校
7 . 我们可以把平面向量坐标的概念推广为“复向量”,即可将有序复数对
视为一个向量,记作
.类比平面向量的线性运算可以定义复向量的线性运算;两个复向量
,
的数量积记作
,定义为
;复向量
的模定义为
.
(1)设
,
,求复向量
与
的模;
(2)已知对任意的实向量
与
,都有
,当且仅当
与
平行时取等号;
①求证:对任意实数a,b,c,d,不等式
成立,并写出此不等式的取等条件;
②求证:对任意两个复向量
与
,不等式
仍然成立;
(3)当
时,称复向量
与
平行.设
,
,
,若复向量
与
平行,求复数z的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20b691a717378e3d8190ae22dcfac98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2adcabafb9c785403537056956f8ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2adcabafb9c785403537056956f8ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f78ec4dc660466c71c79c688f8bbf49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc49dd09fc7dda38a4de6ad364580512.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21a8efc21764c68641ca8a870cff10f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb467f8f90ba3c6ed8dcd5e9b385c5c0.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bb5d6f118bc0f8ca3f73d3c2e93804f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e46d773a664a544127aae7eb8374e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
(2)已知对任意的实向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7f2b6e510313331fd7c781e3837b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
①求证:对任意实数a,b,c,d,不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a8f3b9c67bee7fd6b1312a57a6795a.png)
②求证:对任意两个复向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee7f2b6e510313331fd7c781e3837b37.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66114f41d0e72a29cd584844a432f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4e71ddc3533ffdeb7c4feb9ac23099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47066ed3effe45f5e5d9fd9fc1faa2b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707aed47159fae11f47e464c548a0b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2780422eefb9e85b89074a1ba2a159d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433a8c622b44e1aa29e9989e6978dd7b.png)
您最近一年使用:0次
解题方法
8 . 如图,已知正方体
的棱长为1,E为
的中点,P为对角线上
的一个动点,过P作与平面ACE平行的平面,则此平面截正方体所得的截面( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/1205f59e-9d55-4904-923a-80e402aec6b5.png?resizew=185)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a46a98f42df8dd1d7ba89fe7e6961a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a7bcc1efb8a2ff57d64b6d057da463.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/27/1205f59e-9d55-4904-923a-80e402aec6b5.png?resizew=185)
A.截面不可能是五边形 |
B.截面可以是正六边形 |
C.P从D点向![]() |
D.截面面积的最大值为![]() |
您最近一年使用:0次
名校
解题方法
9 . 已知正四面体
棱长为2,点
分别是
,
,
内切圆上的动点,现有下列四个命题:
①对于任意点
,都存在点
,使
;
②存在
,使直线
平面
;
③当
最小时,三棱锥
的体积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
④当
最大时,顶点
到平面
的距离的最大值为
.
其中正确的有___________ .(填选正确的序号即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7807638578edd712265463a7a5eab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
①对于任意点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c89d54457ad06f095a8643cf3c77923.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e39cbda9b51329928487a7462cb550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b9ffc9d4fbb08792f487b787c71c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d919276bf6174bdf850673cd38284cda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0467b0675c3ecfb282cc88255284d3e1.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6b9ffc9d4fbb08792f487b787c71c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56448a74c1b8430c425d79d626764f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
其中正确的有
您最近一年使用:0次
2024-06-05更新
|
358次组卷
|
2卷引用:辽宁省部分高中2023-2024学年高三下学期第三次模拟考试数学试题
名校
解题方法
10 . 已知常数
数列
的前
项和为
,
且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea73a8c287424d6281822f8a340106e6.png)
(1)求数列
的通项公式;
(2)若
且数列
是单调递增数列,求实数
的取值范围;
(3)若
数列
满足:
对于任意给定的正整数
,是否存在
使
?若存在,求
的值(只要写出一组即可);若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01592e40f9c9db0bf3cceb585a2b9dd.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/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea73a8c287424d6281822f8a340106e6.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6678c59e26c0bea46f44e1aeb3d15422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45051c4c45caa2bf4763206d5708bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8881be0063af5f5008a97ff17a4681da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a5dde3668a8dcc447724aa738bdbdbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e62f7e42856aa40f3b1a1d8890762cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
您最近一年使用:0次