1 . 已知定义域为
的函数
,其图象是连续的曲线,且存在定义域也为
的导函数
.
(1)求函数
在点
的切线方程;
(2)已知
,当
与
满足什么条件时,存在非零实数
,对任意的实数
使得
恒成立?
(3)若函数
是奇函数,且满足
.试判断
对任意的实数
是否恒成立,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851c68ef2e0703706f3b528daa902eb8.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d0d5f2bae6b38d6877b8b40865e834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3832d863e6cefdfe45cff4319e1fbdb.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a48a3e7a13ec19e1ba5ba54e520c76df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e06618e1fff402ca9269e10a396532f.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e084f839e9b7a03fea8b0b596674fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ddc12af8da0819a120eaae5858c4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
解题方法
2 . 我们知道,二维空间(平面)向量可用二元有序数组
表示;三维空间向盘可用三元有序数组
表示.一般地,
维空间向量用
元有序数组
表示,其中
称为空间向量的第
个分量,
为这个分量的下标.对于
维空间向量
,定义集合
.记
的元素的个数为
(约定空集的元素个数为0).
(1)若空间向量
,求
及
;
(2)对于空间向量
.若
,求证:
,若
,则
;
(3)若空间向量
的坐标满足
,当
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1acd1459dd96e861e6e04abccb2a3817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c2a29087dbd2e7635da13f7d288c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a3c6c6fe94124d76957d9a8c837701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8715a3f984d2627afd7c40c61347b7cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc4e5fb9e41d1310778b0dda692066dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afad70ea217c830631639e8508ad410b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0196cb738ee760339a9e15c8e6d9a41.png)
(1)若空间向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4517944d03f267b87ee1c184f463dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a0d7cdd1e3a38753d1290d9de9f9af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc51f796615bfd474cee9d4d80e1eae.png)
(2)对于空间向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09611387d4de23004d388c9a8dde3438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daee8af73118698c77e022651f69ef22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b71af6590f0f369c164a054a8b63bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a205f096c854a2f7cd71255056f9f7.png)
(3)若空间向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd074bea5f4eb8f60729b75e970afda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3894099d6bf29b73086842a48da10174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1653bed33a88140f16d494e8454f5225.png)
您最近一年使用:0次
3 . 设集合
是一个非空数集,对任意
,定义
,称
为集合
的一个度量,称集合
为一个对于度量
而言的度量空间,该度量空间记为
.
定义1:若
是度量空间
上的一个函数,且存在
,使得对任意
,均有:
,则称
是度量空间
上的一个“压缩函数”.
定义2:记无穷数列
为
,若
是度量空间
上的数列,且对任意正实数
,都存在一个正整数
,使得对任意正整数
,均有
,则称
是度量空间
上的一个“基本数列”.
(1)设
,证明:
是度量空间
上的一个“压缩函数”;
(2)已知
是度量空间
上的一个压缩函数,且
,定义
,
,证明:
为度量空间
上的一个“基本数列”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9661053f3ef4cfa926e5d5fd5c6555f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a1f35848a78a4f00c21500e2610e21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171102a883b22fe6ca578efc8926f5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/171102a883b22fe6ca578efc8926f5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c975849cb845a1eb30e25d6bb0782075.png)
定义1:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974cd5eed14d5002f6155dced3e62432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c975849cb845a1eb30e25d6bb0782075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034e4d52bd5ae47074a93c0647f67399.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9661053f3ef4cfa926e5d5fd5c6555f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f1ada25dccde00dfff2525360188a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c975849cb845a1eb30e25d6bb0782075.png)
定义2:记无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da889327e4b9a31336a88e6da53334d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7968de1fe9004760db9a41c24df809b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7968de1fe9004760db9a41c24df809b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c975849cb845a1eb30e25d6bb0782075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/859cf5bf57a50d2da19c0bb926ce9c18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e61e145e5a49ebbe72c3b9ba1f7cdde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a6f5c5649285cbabda20a452db04f38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7968de1fe9004760db9a41c24df809b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c975849cb845a1eb30e25d6bb0782075.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8557a6d85a35cd171e43087afd1b0576.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c95a62ca5cb2f440792632ec36595b.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd6ebf0a370d321e89a8f9921041a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae4c872929a492d8bcd9e649f190a66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8671bcd155dd76d76d83573c6f20e930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cfb19f0c37a72b33083ae9319f11a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6961967d7e48061a9cbb14f597e73d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7968de1fe9004760db9a41c24df809b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae4c872929a492d8bcd9e649f190a66.png)
您最近一年使用:0次
4 . 已知函数
,若数列
的各项由以下算法得到:
①任取
(其中
),并令正整数
;
②求函数
图象在
处的切线在
轴上的截距
;
③判断
是否成立,若成立,执行第④步;若不成立,跳至第⑤步;
④令
,返回第②步;
⑤结束算法,确定数列
的项依次为
.
根据以上信息回答下列问题:
(1)求证:
;
(2)是否存在实数
使得
为等差数列,若存在,求出数列
的项数
;若不存在,请说明理由.参考数据:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71601a0573a3d598bea17f989570fd59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
①任取
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd3ecf27b4de4d36c92c072b17a2a37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
②求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d896b1e6cadb21a23acb227c18b238b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b8d5b6045219ea4527202ab131bb2e.png)
③判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a11ef454b69c4ce4fd731b6f2ec13d70.png)
④令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2583433b021057d8bf772e20f9420a.png)
⑤结束算法,确定数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a94ba3f4906ba526f9f6676540a99b6.png)
根据以上信息回答下列问题:
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72bedf7ef340c4cb9522106f53ef5f37.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb6e83865e833f866807dfbced86dc9.png)
您最近一年使用:0次
5 . 已知定义在
上的函数
的表达式为
,其所有的零点按从小到大的顺序组成数列
(
).
(1)求函数
在区间
上的值域;
(2)求证:函数
在区间
(
)上有且仅有一个零点;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d9eebb0705256305ab3bf28898fffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df075cd20f79486d88d80ee12fc897d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e976c0663fa749ca749f99842d21ca03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b6a6e136f1f05417c93473d27a5efe.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71163f419555f2ed76075c8ff659fbfc.png)
(2)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85fa35905c7193c20799ed7b925b358a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b6a6e136f1f05417c93473d27a5efe.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0710952d6f8d8f6c0de73c42f4301c79.png)
您最近一年使用:0次
名校
解题方法
6 . 对于
,
,
不是10的整数倍,且
,则称
为
级十全十美数.已知数列
满足:
,
,
.
(1)若
为等比数列,求
;
(2)求在
,
,
,…,
中,3级十全十美数的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b1cfbfdf8e1b22aab9583e12e3449c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f0e26992724eafcba06d163d9ff470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4217b1854fee34983372bf4f3a877d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5873c01192b7d33b7483f444f90b5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdf53108bee755f5aa9a34ea4d163e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5c2b5e218eb815213d8bc0ce9a06ca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ac416116febcf793fee4ccc78a27b15.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0f62daf8552adeb241c9b54a57cd83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11075f2c574b6c59b97fb3038000e38.png)
您最近一年使用:0次
2024-05-14更新
|
758次组卷
|
5卷引用:第4套 新高考全真模拟卷(三模重组)
2024高一下·全国·专题练习
7 . 为了调查某班学生每天完成家庭作业所需的时间,在该班随机抽查了8名学生,他们每天完成家庭作业所需时间(单位:分钟)分别为60,55,75,55,55,43,65,40.
(1)求这组样本观测数据的平均数;
(2)估计该班学生每天完成家庭作业的平均时间,按照学校要求,学生每天完成家庭作业所需的平均时间不能超过60分钟,该班学生每天完成家庭作业的平均时间是否符合学校的要求?
(1)求这组样本观测数据的平均数;
(2)估计该班学生每天完成家庭作业的平均时间,按照学校要求,学生每天完成家庭作业所需的平均时间不能超过60分钟,该班学生每天完成家庭作业的平均时间是否符合学校的要求?
您最近一年使用:0次
2024高三·全国·专题练习
8 . 对于数对序列
, 记
,
其中
表示
和
两个数中最大的数,
(1)对于数对序列
, 求
的值
(2)记m为a、b、c、d四个数中最小的数, 对于由两个数对(a, b), (c, d)组成的数对序列
和
, 试分别对m=a和m=d时两种情况比较
和
的大小
(3)在由5个数对(11, 8), (5, 2), (16, 11), (11, 11), (4, 6)组成的所有数对序列中, 写出一个数对序列P使
最小, 并写出
的值(只需写出结论).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3730b8da80bf83e139d6f2d6431e26fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcf9a27f4aed79c1fd9ef8d15fe0d66e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3aed1d5b877fe312c64942a1a4611eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ac724a0f7a5e3bb92f78d639b805eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d3e4bf1f333fbf630ad1750d9a61ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1433338626912da998383a1988052cdc.png)
(1)对于数对序列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d76ac485f6b79bef518f8750953fc99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2159dad0a02fd2545166b1f11eae990.png)
(2)记m为a、b、c、d四个数中最小的数, 对于由两个数对(a, b), (c, d)组成的数对序列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e9eb00b35d29d8f97c4b86a02a5b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b8896c67827fd8f6d11248f7d0a61f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c58446046e1d26e7db0d85cf799a64f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e11ae81a29ebc46e60dacd34f2afa667.png)
(3)在由5个数对(11, 8), (5, 2), (16, 11), (11, 11), (4, 6)组成的所有数对序列中, 写出一个数对序列P使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983db6139d32e042c0018c0901a4bd70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983db6139d32e042c0018c0901a4bd70.png)
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2024高一下·全国·专题练习
9 . 某灯泡厂为测量一批灯泡的使用寿命,从中随机抽查了20只灯泡,它们的使用寿命(单位:h)如下所示:
624 847 1205 698 1845 2457 618 1325 1908 2426
2018 2248 2465 2576 987 737 1628 1998 2543 2007
由这些样本观测数据,估计这批灯泡的平均使用寿命.
624 847 1205 698 1845 2457 618 1325 1908 2426
2018 2248 2465 2576 987 737 1628 1998 2543 2007
由这些样本观测数据,估计这批灯泡的平均使用寿命.
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名校
10 . 五月初,某中学举行了“庆祝劳动光荣,共绘五一华章”主题征文活动,旨在通过文字的力量,展现劳动者的风采,传递劳动之美,弘扬劳动精神.征文筛选由A、B、C三名老师负责.首先由A、B两位老师对征文进行初审,若两位老师均审核通过,则征文通过筛选;若均审核不通过,则征文落选;若只有一名老师审核通过,则由老师C进行复审,复审合格才能通过筛选.已知每篇征文通过A、B、C三位老师审核的概率分别为
,且各老师的审核互不影响.
(1)已知某篇征文通过筛选,求它经过了复审的概率;
(2)从投稿的征文中抽出4篇,设其中通过筛选的篇数为X,求X的分布列和数学期望.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7178ffcb231a6000b334881a104c585.png)
(1)已知某篇征文通过筛选,求它经过了复审的概率;
(2)从投稿的征文中抽出4篇,设其中通过筛选的篇数为X,求X的分布列和数学期望.
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2024-05-12更新
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1579次组卷
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3卷引用:易错点9 概率类型定不准致误