名校
1 . 有甲乙两个骰子,甲骰子正常且均匀,乙骰子不正常且不均匀,经测试,投掷乙骰子得到6点朝上的概率为
,若投掷乙骰子共6次,设恰有3次得到6点朝上的概率为
,
是
的极大值点.
(1)求
;
(2)若
且等可能地选择甲乙其中的一个骰子,连续投掷3次,在得到都是6点朝上的结果的前提下,求这个骰子是乙骰子的概率;
(3)若
且每次都等可能地选择其中一个骰子,共投掷了10次,在得到都是6点朝上的结果的前提下,设这10次中有
次用了乙骰子的概率为
,试问当
取何值时
最大?并求
的最大值(精确到0.01).(参考数据
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f109f79547d6ae0d94339e689e8f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1f109f79547d6ae0d94339e689e8f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098e663b79254b0a2e0e00f92bd14b8d.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098e663b79254b0a2e0e00f92bd14b8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e97dd472fe7779d5c729aa8dedd99190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcbd28fefa404513768b10747e2291a.png)
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真题
2 . 已知集合
.给定数列
,和序列
,其中
,对数列
进行如下变换:将
的第
项均加1,其余项不变,得到的数列记作
;将
的第
项均加1,其余项不变,得到数列记作
;……;以此类推,得到
,简记为
.
(1)给定数列
和序列
,写出
;
(2)是否存在序列
,使得
为
,若存在,写出一个符合条件的
;若不存在,请说明理由;
(3)若数列
的各项均为正整数,且
为偶数,求证:“存在序列
,使得
的各项都相等”的充要条件为“
”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd62e1c433cfb342fcd7f334ccc968f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1039be74acc3366c11fae59651f85d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3fd26c26f6f07fabfa38eccf3d2fc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89441a335677dbf88779bbb65c543375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dcedacb9353214d02e5f6c7e693ac7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9353bc48a30bbf4d807d858c4604b1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9353bc48a30bbf4d807d858c4604b1c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6995fd4ede4b441f54a1e0996447ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6caacfd319814df87257a1823d8e801c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb7fbd87354b2529d4f0a155fad1b2cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62089081cbcb03a9495a3061b8570f60.png)
(1)给定数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52596c7a4a85221a0edb36591bd6a9e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4d9ec580a62b48148a48c711794a6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62089081cbcb03a9495a3061b8570f60.png)
(2)是否存在序列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62089081cbcb03a9495a3061b8570f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d5d87042c71d41b61ee416d4f79724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a766e037468d9c6e4bade3de283ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa35373ec4e4684107b42adb7a5161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62089081cbcb03a9495a3061b8570f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666ba875a2642bbec1fdfcdab8e4e62d.png)
您最近一年使用:0次
3 . 已知两条抛物线
,
.
(1)求
与
在第一象限的交点的坐标.
(2)已知点A,B,C都在曲线
上,直线AB和AC均与
相切.
(ⅰ)求证:直线BC也与
相切.
(ⅱ)设直线AB,AC,BC分别与曲线
相切于D,E,F三点,记
的面积为
,
的面积为
.试判断
是否为定值,若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8a3bffe545af2299cf999d44767206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d1138c04fc3a0e1c217db0d432e4aff.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知点A,B,C都在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(ⅰ)求证:直线BC也与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(ⅱ)设直线AB,AC,BC分别与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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4 . 已知函数
,且
在
上的最小值为0.
(1)求实数
的取值范围;
(2)设函数
在区间
上的导函数为
,若
对任意实数
恒成立,则称函数
在区间
上具有性质
.
(i)求证:函数
在
上具有性质
;
(ii)记
,其中
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55386df48bce6389f5ea9dd827b2600d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d65bdc820ab87b9a7909d2be591abec.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b81a631c1fcd5fa6986baca8c7f754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277a2bf55ddf8cf07f22b2128712e2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08653fc03ff2c4ccaf3ab8b18474ee17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b81a631c1fcd5fa6986baca8c7f754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(i)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b672f564d03ed46d092bb130f229ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9626dc41063c34f4243b5a637668b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(ii)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88209b9c5c9503721afc5696b8943a10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2f05512a14030b8a9cd9c118ed962f.png)
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名校
5 . 已知函数
,
.
(1)若直线
是曲线
在
处的切线,求
的表达式;
(2)若任意
且
,有
恒成立,求符合要求的数对
组成的集合;
(3)当
时,方程
在区间
上恰有1个解,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b923078510697d5f7f9ea392eb76dd9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4935611969e644511329f6b0dbbf3b.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/779857e2a9f13158fb4cf5988debceca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)若任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5223ece2f8f76850c49e2505304532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eaa16e4de765a7127b2a4aa8302cef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a5286cdf08218995b1514c195494e3.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143b917df0520097be222accbddf9394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/298b861acdad2f218a882319c1a3280a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a531b9769bfba66a10139b153f09307c.png)
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6 . 已知数列
,
,函数
,其中
,
均为实数.
(1)若
,
,
,
,
,
(ⅰ)求数列
的通项公式;
(ⅱ)设数列
的前
项和为
,求证:
.
(2)若
为奇函数,
,
,
且
,问:当
时,是否存在整数
,使得
成立.若存在,求出
的最大值;若不存在,请说明理由.(附:
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2b44ac9ffc5dd71901d5cae704f059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f2599ca8b6b683e57a82699c8b1ebb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b970d657304931a9d5cecdb044968f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a783088120d67cc98936081e80fb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32003b56a60c9977c5d5d667c4136f62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385275d29d8c8a7841eaeaa3dfab2cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b14938503c29201f32d30deda61db3.png)
(ⅰ)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
(ⅱ)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411bfe81694849b77de8b87f2651975a.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/43af3d8ebe0e5f0a905d42d29afe6f6f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e442aaf3fda101960c18cc41de1614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d39c60d4618060bbdc332282f0a0dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f7cc67b3e263a2562be3c4c80dd5a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfb7ad7e6f4bbe0ec8dc3bec7d49025.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/570c49bcd783ed65a16b7bc565347094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e474d29ab7f3a4e404f593e90ae8b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c1868215cf7dbeb9dd228d2cede3e9.png)
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名校
解题方法
7 . 设点集
,从集合
中任取两个不同的点
,
,定义A,
两点间的距离
.
(1)求
中
的点对的个数;
(2)从集合
中任取两个不同的点A,
,用随机变量
表示他们之间的距离
,
①求
的分布列与期望;
②证明:当
足够大时,
.(注:当
足够大时,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3afcb129040d060714f94c0f8c48a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c6d29b3010fc1dc9cb640ad41d5b97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8034add7b8011393a866a21479b62f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ebc8c7e32c1b561a908a36cfa2cbb5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32efe4eff75508cb93e828c735dcb695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ffbdfab9dff3ff41ea474f06375032.png)
(2)从集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ddad3d9fdb5e9951b6a1c31f9a72a71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb4828b16c8e845492f1a53ddd9a9.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
②证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59306134d26d7a35fd18bcdd401faeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8eed2b9b1f33517499ef35e044cd104.png)
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7日内更新
|
601次组卷
|
2卷引用:山东省临沂市兰山区等四县区2024届高三第三次模拟考试数学试题
名校
8 . 已知有穷正项数列
,若将每个项依次围成一圈,满足每一项的平方等于相邻两项平方的乘积,则称该数列可围成一个“HL-Circle”.例如:数列
都可围成“HL-Circle”.
(1)设
,当
时,是否存在
使该数列可围成“HL-Circle”,并说明理由:
(2)若
的各项不全相等,且可围成“HL-Circle”.
(i)求
的取值集合;
(ii)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a2723483435ce9c39acae4032d12e9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec293ea5d248edf3b66a54f81b5e5f0.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7fab51121848ce166035ceab6f4e00b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7a1d739890a8951586e23b78b035bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9989990eebe2cc2bdddafd5e1d6c0a85.png)
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名校
9 . 若曲线C的切线l与曲线C共有n个公共点(其中
,
),则称l为曲线C的“
”.
(1)若曲线
在点
处的切线为
,另一个公共点的坐标为
,求
的值;
(2)求曲线
所有
的方程;
(3)设
,是否存在
,使得曲线
在点
处的切线为
?若存在,探究满足条件的t的个数,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a4e961d362e7454658bad29750a1cd.png)
(1)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48befa5d90fafd8bfdb6c90fd241ebfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/567c7a1edad2de8d71a06eb76c8b52b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad42625f296d2a4b65180e2f7b776beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/680c514271ab4a9c8424873bd5e2b154.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d395a5e66576b31ba39a2abcecc26d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0a442bb3027296d45df4b72609b5d02.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d71f56ef6906bc37ca312051d97d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce71911f990a0d69b54c6ca453ac9a93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56849f3da518eff9bf32c7149f9d49b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0520cf6db4ec82dc0e092f2aa0036427.png)
您最近一年使用:0次
10 . 对于平面向量
,定义“
变换”:
,其中
表示
中较大的一个数,
表示
中较小的一个数.若
,则
.记
.
(1)若
,求
及
;
(2)已知
,将
经过
次
变换后,
最小,求
的最小值;
(3)证明:对任意
,经过若干次
变换后,必存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fde5542ad04744c14f912648f3aa0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41bd66e602e9c043218806708e943c2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb00071815c94c090a4095b4964fefb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7bc9573b3a8758511c63731db18183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96340894e8fb63c00d778b4d654d0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7bc9573b3a8758511c63731db18183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701ab98a2bf1135cd989822b0738e11d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/484c1b7bc2fc5677406e20180f667200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0624499e16b73afec432dd1afd6153d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b162d1d5bfaa7760678ea3d624beb171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5c19921380da55f5f1a00809a34503.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35234a3829d238ea479fef9cec166468.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aceb3666a9d49ef40c39eac116ccd5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20cfb8c8707c3960bf1fd46b805e481d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a887552671e6d4df390320ee9a36150.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)证明:对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f389ec068eb1d1aa586b79097d70a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dcd78ec8777a8e6e5b32222cdb15c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06296b9023c1dca6f44b8297842bef7c.png)
您最近一年使用:0次