名校
1 . 记集合
.对任意
,
,记
,对于非空集合
,定义集合
.
(1)当
时,写出集合
;对于
,写出
;
(2)当
时,如果
,求
的最小值;
(3)求证:
.
(注:本题中,
表示有限集合A中的元素的个数.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a89f895a14b4f202dfe6b19224857c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74c86c0b2a71ee538df6ab1eab3c8b2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd58ba2338450bd94bc2a1ec0a0a51ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120df58b92e747fc3091f1a3aeff228d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13342dd73eb34ca37aaca5b521706442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ca324ae5ead82dd03b6cb5afac67a5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4469a0542c773e329e8cc42e14a84169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0ca0b9e99203ec575c46cdbf2d4ef0d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8839c83b988c42da1fce4a96787583eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c045c7a097a2908732932f4c0c170693.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25376e139f40d0df5ada2c9ebb1da2e4.png)
(注:本题中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c045c7a097a2908732932f4c0c170693.png)
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2 . 对于正整数n,
是小于或等于n的正整数中与n互质的数的数目.函数
以其首名研究者欧拉命名,称为欧拉函数,例如
(
与
互质),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7cc0ad7521b5771950aea983f0c1c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7cc0ad7521b5771950aea983f0c1c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c9e69c7d5a3d7a5633a373a8a39544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786c6406780167f9744d0f9e9682e471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d02ea8c4988c5c28ab93f0d70fb55a.png)
A.若n为质数,则![]() | B.数列![]() |
C.数列![]() | D.数列![]() |
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3卷引用:湖北省宜荆荆2024届高三下学期五月高考适应性考试数学试题
湖北省宜荆荆2024届高三下学期五月高考适应性考试数学试题 吉林省通化市梅河口市第五中学2024届高三三模数学试题(已下线)高二数学期末模拟试卷02【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)
名校
3 . 在数学中,由
个数
排列成的m行n列的数表
称为
矩阵,其中
称为矩阵A的第i行第j列的元素.矩阵乘法是指对于两个矩阵A和B,如果4的列数等于B的行数,则可以把A和B相乘,具体来说:若
,
,则
,其中
.已知
,函数
.
(1)讨论
的单调性;
(2)若
是
的两个极值点,证明:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db452ec3c9e60109fdfe9fae8e456edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc970ba32a45946c514e98eac1e80ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e70354d6ca5ad9f6b4592fac0b5e559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37a14c188b1c9d61aa237b137ba18023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16a9a7e6a7ff34bb72659677929bf9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7cf279527982a84842a2d6a4f212892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b65887e38142a10f30be2296310d1a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9408afcaa76f52987ca43733b828f66a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01f44187cd898fb01a4f8fa76bdc6cdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8d8e4e3f777270997845f7d9cfe85f.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3db0fe99d90b9a693562dd988eca5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def4d3923ea803696106f42140e83bf4.png)
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3卷引用:山东省泰安市2024届高三四轮检测数学试题
山东省泰安市2024届高三四轮检测数学试题江西省宜春市宜丰中学2023-2024学年高二下学期6月月考数学试题(已下线)高二数学期末模拟试卷01【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(北师大版2019选择性必修第二册)
名校
解题方法
4 . 设定义域为
的函数
在
上可导,导函数为
.若区间
及实数
满足:
对任意
成立,则称函数
为
上的“
函数”.
(1)判断
是否为
上的
函数,说明理由;
(2)若实数
满足:
为
上的
函数,求
的取值范围;
(3)已知函数
存在最大值.对于:
:对任意
与
恒成立,
:对任意正整数
都是
上的
函数,问:
是否为
的充分条件?
是否为
的必要条件?证明你的结论.
![](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/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851c68ef2e0703706f3b528daa902eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b639b31035fc3862454ff8ce2b9a5154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bb6324279df94decba955e04ccfa9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6c26e485c3956d1576524fbc17927f.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db76af819439f36b33fd89b7911a45cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd50020c0e3198d4a6b2d26a413b1b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f352df4a168a31caef9c4e017dae0d74.png)
(2)若实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3162d2c7b650bba3e401ffbb1e13bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b34e8d8b62a1d94748c849f066406169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6c26e485c3956d1576524fbc17927f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b968a1d9d735d2482aef72fb73e9707a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58196b9e63ec00aa1119052b6de6ae12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e9f933b77561af59f821a9f7bd46b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca89e1424190793ebcd3944d73e25c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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2024·全国·模拟预测
5 . 甲、乙两名小朋友,每人手中各有3张龙年纪念卡片,其中甲手中的3张卡片为1张金色和2张银色,乙手中的3张卡片都是金色的,现在两人各从自己的卡片中随机取1张,去与对方交换,重复
次这样的操作,记甲手中银色纪念卡片
张,恰有2张银色纪念卡片的概率为
,恰有1张银色纪念卡片的概率为
.
(1)求
的值.
(2)问操作几次甲手中银色纪念卡片就可能首次出现0张,求首次出现这种情况的概率
.
(3)记
.
(i)证明数列
为等比数列,并求出
的通项公式.
(ii)求
的分布列及数学期望.(用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ffb021aa7d5a5c2f0691e337caad624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce603aa3abcb61750d2191aaa13dddc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f66b7e38f44f8cd5d48b3aa24a20fc.png)
(2)问操作几次甲手中银色纪念卡片就可能首次出现0张,求首次出现这种情况的概率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9131abf93295537bbc0c54a8c42e88e2.png)
(i)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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名校
解题方法
6 . 已知双曲线
的实轴长为2,顶点到渐近线的距离为
.
(1)求双曲线
的标准方程;
(2)若直线
与
的右支及渐近线的交点自上而下依次为
,证明:
;
(3)求二元二次方程
的正整数解
,可先找到初始解
,其中
为所有解
中的最小值,因为
,所以
;因为
,所以
;重复上述过程,因为
与
的展开式中,不含
的部分相等,含
的部分互为相反数,故可设
,所以
.若方程
的正整数解为
,则
的面积是否为定值?若是,请求出该定值,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390f2c99d60abc83d9bda1a79995486f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1af14f9a53cb0f07d5d28dceba30aa.png)
(3)求二元二次方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6ad120ce64035347eb7325fae9617c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb81c100a8985b5cfc606dc60cacd5ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56720e2f2b0ddd72156da495923698da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5acbd95efd8b0cb3e108fce6dc02af80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f4d959c570141afd7d0d6abc3969012.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d350c9707efa6d8bb584395ccc07dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bd475f0c71e7e8c66fad3642779dc7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d694975be0ce869d210e18f85e583f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e9c5a319966741ff9c3b52fb4de883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c8e7b7827e1735c45c1e5ce59cdd624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3460cd2f27a53941986606734a9b479a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3460cd2f27a53941986606734a9b479a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b66d595bfea3722fbc56e2fdccd548.png)
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名校
解题方法
7 . 在平面直角坐标系中,确定若干个点,点的横、纵坐标均取自集合
,这样的点共有n个.
(1)求以这n个点中的2个点为端点的线段的条数;
(2)求这n个点能确定的直线的条数;
(3)若从这n个点中选出3个点分别为三角形的3个顶点,求这样的三角形的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109fea550364bb2aabef823b83ccb37c.png)
(1)求以这n个点中的2个点为端点的线段的条数;
(2)求这n个点能确定的直线的条数;
(3)若从这n个点中选出3个点分别为三角形的3个顶点,求这样的三角形的个数.
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名校
8 . 甲乙两人参加知识竞赛活动,比赛规则如下:两人轮流随机抽题作答,答对积1分且对方不得分,答错不得分且对方积1分,然后换对方抽题作答,直到有领先2分者晋级,比赛结束.已知甲答对题目的概率为
,乙答对题目的概率为P,答对与否相互独立,抽签决定首次答题方,已知两次答题后甲乙两人各积1分的概率为
.记甲乙两人的答题总次数为
.
(1)求P;
(2)当
时,求甲得分X的分布列及数学期望;
(3)若答题的总次数为n时,甲晋级的概率为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7294f5ae2a24ff42e84cd9773b2a7287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac97e6740365c85ad857aff85cefbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3b5b9038b39e659fdade4a5063edad.png)
(1)求P;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c9d7f7f9a3e9ec476f5cf7fda97c88.png)
(3)若答题的总次数为n时,甲晋级的概率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb61ad9ef2dcb36f21d5979e21cfe10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b63edd22b23f84960e7c5e07102e0b9.png)
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名校
9 . 代数基本定理:任何一个
次复系数多项式方程
至少有一个复根.由此可得如下推论:
推论一:任何一元
次复系数多项式
在复数集中可以分解为
个一次因式的乘积;
推论二:一元
次多项式方程有
个复数根,最多有
个不同的根.即一元一次方程最多有1个实根,一元二次方程最多有2个实根等.
推论三:若一个
次方程有不少于
个不同的根,则必有各项的系数均为0.
已知
.请利用代数基本定理及其推论解决以下问题:
(1)求
的复根;
(2)若
,使得关于
的方程
至少有四个不同的实根,求
的值;
(3)若
的图像上有四个不同的点
,以此为顶点构成菱形
,设
,
,求代数式
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab009a153dfcc13ba9eb4916c76f8ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b7bff9b2431134f7683a9cc4e68acd.png)
推论一:任何一元
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab009a153dfcc13ba9eb4916c76f8ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
推论二:一元
![](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/b6a24198bd04c29321ae5dc5a28fe421.png)
推论三:若一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14c686bfce270ec65d068555d1866ff.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dadabea3f5008d97a32382752e62bdd8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ec4e65c4c043edef8084b292675395c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcecb855c13987b207aec2db73c9ec5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc04eee630e386f7be4ac709ff4e16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df74fc4cedb204eb6dcce64b706e99c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0c942fae0e9dd2d219ad8269511898.png)
您最近一年使用:0次
10 . 定义:若函数
与
的图象在
上有且仅有一个交点,则称函数
与
在
上单交,此交点被称为“单交点”.已知函数
,
,
.
(1)讨论函数
的单调性;
(2)当
时,
(i)求证:函数
与
在
上存在“单交点”
;
(ⅱ)对于(i)中的正数
,证明:
.
![](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/b3eb5935678e432e6f1f3180bfdb3175.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/b3eb5935678e432e6f1f3180bfdb3175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ba24231723af1ea3d94be78053998f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e19cdacdd4a47291e4621a8c167efc.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e455f4e6c97270bd28f207b89df5fa.png)
(i)求证:函数
![](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/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
(ⅱ)对于(i)中的正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33e33f6cdfee603b548e158bcb1f82df.png)
您最近一年使用:0次