名校
解题方法
1 . 对于函数
,
,如果存在一组常数
,
,…,
(其中k为正整数,且
)使得当x取任意值时,有
则称函数
为“k级周天函数”.
(1)判断下列函数是否是“2级周天函数”,并说明理由:①
;②
;
(2)求证:当
时,
是“3级周天函数”;
(3)设函数
,其中b,c,d是不全为0的实数且存在
,使得
,证明:存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851eae00e3369068e33a7e6420483883.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f7f4cc0837a4e6dcd0072887e4e2704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe6d9f54a34762aadfdf8e2bac977cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01d28d20e26e8b1dee2848daf6baf0ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)判断下列函数是否是“2级周天函数”,并说明理由:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/903ce67dc4e5bfb0dee630c072664bdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc833417345710524c29cf0d8a9384d.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a91b27ee76da8dcec88eba1b230bfa19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbbcdfbc54530814e37819fc7c93cc07.png)
(3)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e159058cf3cbdf0dd54fa0ab50b58c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df307146ad61d4bf105370f65a3e742c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf90b80e784747a72920eb34d17ddbeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ddf844e3848b8bf52c0ec506fe749c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07534f9e1dc7abca543e655e05db1e50.png)
您最近一年使用:0次
名校
解题方法
2 . 若函数
图像上存在相异的两点P、Q,使得函数
在点P和点Q处的切线重合,则称
是“双切函数”,点P、Q为“双切点”,直线PQ为
的“双切线”.
(1)若
,判断函数
是否为“双切函数”,并说明理由;
(2)若
,证明:函数
是“双切函数”,并求出其“双切线”;
(3)
,求证:“
”是“双切函数”的充要条件是“
”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/548119e2b5a0205515df991c63f160be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76883161fd2bccf1416aeab0200d7e16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2601b3958141a4c279eee4ad9e28bf1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eef90305c5a14c11d9d4c42b7b22f38e.png)
您最近一年使用:0次
名校
3 . 定理(三角不等式),对于任意的
、
,恒有
.定义:已知
且
,对于有序数组
、
、
、
,称
为有序数组
、
、
、
的波动距离,记作
,即
,请根据上述俼息解决以下几个问题:
(1)求函数
的最小值,并指出函数取到最小值时
的取值范围;
(2)①求有序数组
、
、
、
的波动距离
;
②求证:若
、
、
、
且
,则
;题(注:该命题无需证明,需要时可直接使用).设两两不相等的四个实数
、
、
、
,求有序数组
、
、
、
的波动距离
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd0914dc4d4c7f75710ff460a286fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49506c61cf5c61605f1cf90a440348cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec475a4298eab592d6589aab8915276.png)
![](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/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ef141315bf951ddcd300f0743a16897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7cfd590897d8d908066c781c63a812d.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d3b887215cd1514d3e2e79063729a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)①求有序数组
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7330e52932883877de428cfe91962b96.png)
②求证:若
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a876ecb804eb0553c246e5fcc40b708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b73abfe4bc26b1ded680d7abb1a2cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effb89a4bffb74028211ecfe671b79d1.png)
![](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/d46944e1594eec140cacd7b454342561.png)
![](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/daf464629fa321a6ff7401ab79f07083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc0ce632fa217dc77f6c92afd311815.png)
您最近一年使用:0次
2022-08-22更新
|
417次组卷
|
7卷引用:上海市控江中学2021-2022学年高一上学期期中数学试题
上海市控江中学2021-2022学年高一上学期期中数学试题(已下线)专题02 等式与不等式(练习)-2上海市高桥中学2022-2023学年高一上学期期中数学试题(已下线)期中模拟预测卷03(测试范围:前三章)-2022-2023学年高一数学上学期期中期末考点大串讲(沪教版2020必修第一册)(已下线)上海高一上学期期中【压轴42题专练】(2)(已下线)第二章 等式与不等式(压轴题专练)-速记·巧练(沪教版2020必修第一册)上海市吴淞中学2023-2024学年高一上学期期中数学试题
名校
4 . 已知
为实数.利用反证法证明“已知
,求证:
中,至少有一个数大于20"时,首先要假设结论不对,即就是要假设( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874781ab5711bff6ee8c9cbad5b3b3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7267291073b77eab69d5d01383c045d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874781ab5711bff6ee8c9cbad5b3b3dc.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
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解题方法
5 . 设
,函数
.
(1)若
,求证:函数
是奇函数;
(2)若
,判断并证明函数
的单调性;
(3)设
,
,若存在实数m,n(
),使得函数
在区间[m,n]上的取值范围是
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d04bcc342e046321abc203690916602.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e10e1c43b86a8cd4360ca9b57232164.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a4eaa80b44625890339d6a0065c241.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb7961cbe98aac6a5fdee94582c341b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09b29a7faa14a6e09d0db2d04f4ced03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d45cf196f21e10ce4031d26fefc22f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573eecbc29f522671b3892ec406c50b.png)
您最近一年使用:0次
2022-01-21更新
|
716次组卷
|
8卷引用:上海市控江中学2021-2022学年高一上学期期末数学试题
上海市控江中学2021-2022学年高一上学期期末数学试题江苏省南通市通州、海安2019-2020学年高一上学期期末联考数学试题(已下线)【新东方】在线数学35江苏省南通市通州区金沙中学2020-2021学年高一上学期第二次调研考试数学试题四川省四川师范大学附属中学2021-2022学年高一上学期12月月考数学试题(已下线)第13讲 函数的基本性质(8大考点)(3)(已下线)第13讲 函数的基本性质(8大考点)(2)(已下线)专题14函数的基本性质-【倍速学习法】(沪教版2020必修第一册)
名校
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4749985beebb82af49bf81daed263b91.png)
在区间
上的最大值为
,最小值为
,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764252096a427d22e7806422c0bff54f.png)
;
(1)求实数
、
的值;
(2)若不等式
对任意
恒成立,求实数
的范围;
(3)对于定义在
上的函数
,设
,
,用任意的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
将
划分为
个小区间,其中
,若存在一个常数
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29258a85f75b9cb8b0f950d270165f84.png)
恒成立,则称函数
为
上的有界变差函数;
①试证明函数
是在
上的有界变差函数,并求出
的最小值;
②写出
是在
上的有界变差函数的一个充分条件,使上述结论成为其特例;(不要求证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4749985beebb82af49bf81daed263b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf8197e4f3fd18815045d29c357a863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a248e47163191168a1b363937eebd618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764252096a427d22e7806422c0bff54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3210274e57cc0487a58b99ea274b8aa1.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c5e6b1cf8b9ace30d26f232da3dac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)对于定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1ed40a8f67e93401e544284ceaaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc272934625d1232ad34eedc6b23267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752c287b0680a053e18be60f6e34ebba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1b6d5c6b222d95759ea7d39f0b908f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b09511efe31176effed50209b4aa5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29258a85f75b9cb8b0f950d270165f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fc2920f7b5d960d1a927fed29b6a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1ed40a8f67e93401e544284ceaaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
①试证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da34ce730f711c09909d53806fe2330a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
②写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
您最近一年使用:0次
2020-01-07更新
|
446次组卷
|
2卷引用:上海市控江中学2016-2017学年高三上学期第一次月考数学试题
解题方法
7 . 已知双曲线
,经过点
的直线
与该双曲线交于
两点.
(1)若
与
轴垂直,且
,求
的值;
(2)若
,且
的横坐标之和为
,证明:
.
(3)设直线
与
轴交于点
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e250158df0fcb0b51013bd626545e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ac8fa800c00933279f2b20e5034438.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138c0f0b71a955d0a4f249d57b53d5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71812e0762c0aaffb51cfef66156567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a563c50a7f6d10fa46339d7107fc85e.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb6ee119dc122c6bda124041812a2ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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2020-05-20更新
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508次组卷
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5卷引用:2020届上海杨浦区高三二模数学试题
2020届上海杨浦区高三二模数学试题(已下线)热点04 平面向量、复数-2021年高考数学【热点·重点·难点】专练(上海专用)上海市致远高中2020-2021学年高二上学期12月月考数学试题上海市同济大学第二附属中学2024届高三上学期期中数学试题西藏拉萨市部分学校2023-2024学年高二上学期期末模拟数学试题(理科)
名校
8 . 若函数
满足:对于其定义域
内的任何一个自变量
,都有函数值
,则称函数
在
上封闭.
(1)若下列函数:
,
的定义域为
,试判断其中哪些在
上封闭,并说明理由.
(2)若函数
的定义域为
,是否存在实数
,使得
在其定义域
上封闭?若存在,求出所有
的值,并给出证明;若不存在,请说明理由.
(3)已知函数
在其定义域
上封闭,且单调递增,若
且
,求证:
.
![](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/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbeb3e409144a9614be9adabf420987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)若下列函数:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42f26e4241c63908a3d50de4244eca11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a503d329efc27f634f49d87c799ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a416686ed19ea01d2e58efd200a7c131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ede4f08bda3f2125a9e5848ea63bca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知函数
![](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/f3102c0a2f53b80f9dddbf9352537e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374054f44b9a52668f91ac7601e63c06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f66a2b3d90f0d935d6c8ebaf675349.png)
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2020-02-29更新
|
371次组卷
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4卷引用:上海市复旦大学附属中学2015-2016学年高一上学期期末数学试题
上海市复旦大学附属中学2015-2016学年高一上学期期末数学试题上海市复旦大学附属中学2019-2020学年高一上学期期末数学试题第1章+集合与逻辑(能力提升)-2020-2021学年高一数学(必修一)单元测试定心卷(沪教版2020)(已下线)期末复习【真题训练】-2020-2021学年高一数学单元复习(沪教版2020必修第一册)
9 . 已知数列
满足:
,
,
.
(1)求
的值;
(2)设
,求证:数列
是等比数列,并求出其通项公式;
(3)对任意的
,
,在数列
中是否存在连续的
项构成等差数列?若存在,写出这
项,并证明这
项构成等差数列:若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d5105885529d44d6225c78bc8ec7f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ec0b97655e6bd7004df04457c493ac.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed6fe44bc49b478979589face327799.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8e7288daee78eb216a3d61b4e5c7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
(3)对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72ac49ab7c8001c209b8611b9ea40d85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f6b18b109a656b62fb173680ae99ca7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e77d6f15137ae5d98b0d546672b6f68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e77d6f15137ae5d98b0d546672b6f68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e77d6f15137ae5d98b0d546672b6f68.png)
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名校
10 . 已知数列
满足:
,
,
.
(1)求证:数列
为等差数列,并求出数列
的通项公式;
(2)记
(
),用数学归纳法证明:
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8099bd4e5087d2947ce09ffd7abd86d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8927e6db7dc997cc59ddb0ff5900c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/055f13be5ec5847ebbd46e50c2cca4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42d50acc7fcbee425b4e5598f72fbbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
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