名校
解题方法
1 . 已知函数
,其中
.
(1)判断函数
的奇偶性,并说明理由;
(2)记点
,求证:存在实数
,使得点
在函数
图像上的充要条件是
;
(3)对于给定的非负实数
,求最小的实数
,使得关于
的不等式
对一切
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1374fed1f423cc63574bea0ed380f2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e893793ff42e085e77129eb6af4161.png)
(2)记点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e893793ff42e085e77129eb6af4161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a80d3881e7a8ae2ba2c0cd3a7f47cad.png)
(3)对于给定的非负实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75c04cd253e7ea5d33556f5e9bc7610d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d1f935f799ae17ab87ef17e9faf81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0764a141b433c8f3d90b5821f52c1c3b.png)
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2020-08-07更新
|
475次组卷
|
2卷引用:上海市2022届高考模拟卷(二)数学试题
2 . 若数列
满足
,则称数列
为
数列.记
.
(1)写出一个满足
,且
的
数列
;
(2)若
,证明:
数列
是递增数列的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aad868b3ad02db4cc9f1124f4353dd64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f091041ad6daa356c94a7ad1d62647c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41af24a0baa55b8f596c1b32f77103f0.png)
(1)写出一个满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2750dc9a0ad9b327da7a92f524cb90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2727681733ed1c0eeedacbcad8ab1a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002f030017f6f0b34a61b2e15c5a9cb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f238e789b98853553a4cfb1f07cfbc31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ca967d2f5ea038668c650881de0dfc.png)
您最近一年使用:0次
3 . 写出函数
为奇函数的充要条件,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3e4270cbcf56fb75692f303bb0aa519.png)
您最近一年使用:0次
4 . 若函数
满足“存在正数
,使得对定义域内的每一个值
,在其定义域内都存在
,使
成立”,则称该函数为“依附函数”.
(1)分别判断函数①
,②
是否为“依附函数”,并说明理由;
(2)若函数
的值域为
,求证:“
是‘依附函数’”的充要条件是“
”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9813ba347d835df2bda3f491e4af1a82.png)
(1)分别判断函数①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bee6881a170f6ef9ed5c133b95c2f448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a981aa485843b0c1c197937a1400d026.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e915b67f8f747698b8b46d37bc453667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14f97c1fef6dea43a9cb106a13c5760.png)
您最近一年使用:0次
名校
5 . 已知函数
的定义域为D,若存在实常数
及
,对任意
,当
且
时,都有
成立,则称函数
具有性质
.
(1)判断函数
是否具有性质
,并说明理由;
(2)若函数
具有性质
,求
及
应满足的条件;
(3)已知函数
不存在零点,当
时具有性质
(其中
,
),记
,求证:数列
为等比数列的充要条件是
或
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a12ea6f9d2bbcc5a3d7980dbe79922d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c014d6dd9b1ba0c145f08767a6f522b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08c4c03f81039abf2fec0d1d504e7d28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff8d1a032a46b55227a965e7616b5fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6aa2c51f1ced876167b4f2717c9736a.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6aa2c51f1ced876167b4f2717c9736a.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5079e2f37cefb15856bcaf754505cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6aa2c51f1ced876167b4f2717c9736a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d92fe568c519ab69cfe6088070ea17c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a369ce3949b2bd2747a48054f7b951c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78cac409e814b614cb060b6fc41caa85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389662f03137dce5ad957894ea7d6d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808ef8edf6546fb634a902d50545aaed.png)
您最近一年使用:0次
2020-05-21更新
|
480次组卷
|
4卷引用:2020届上海市松江区高三下学期模拟考质量监控数学试题
2020届上海市松江区高三下学期模拟考质量监控数学试题上海市进才中学2021-2022学年高二下学期3月月考数学试题(已下线)4.3.1.2 等比数列的性质及应用(练习)-2022-2023学年高二数学同步精品课堂(人教A版2019选择性必修第二册)(已下线)4.2 等比数列(第1课时)(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
名校
解题方法
6 . 已知由n(n∈N*)个正整数构成的集合A={a1,a2,…,an}(a1<a2<…<an,n≥3),记SA=a1+a2+…+an,对于任意不大于SA的正整数m,均存在集合A的一个子集,使得该子集的所有元素之和等于m.
(1)求a1,a2的值;
(2)求证:“a1,a2,…,an成等差数列”的充要条件是“
”;
(3)若SA=2020,求n的最小值,并指出n取最小值时an的最大值.
(1)求a1,a2的值;
(2)求证:“a1,a2,…,an成等差数列”的充要条件是“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/858c881d66b4f60b16eb1b6339fed55f.png)
(3)若SA=2020,求n的最小值,并指出n取最小值时an的最大值.
您最近一年使用:0次
2020-05-10更新
|
664次组卷
|
3卷引用:2020届北京八中高三3月学模拟考试数学(二)试题
7 . 已知
都是非零实数,且
,求证:
的充要条件是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b21208364124b5c477b2ff8df1c2e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc539c71b72aff71e7c8e31e74969d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c328c9c4ec69c4275e27576fb61655.png)
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2020-04-11更新
|
2236次组卷
|
21卷引用:对点练02 充分条件与必要条件-2020-2021年新高考高中数学一轮复习对点练
(已下线)对点练02 充分条件与必要条件-2020-2021年新高考高中数学一轮复习对点练1号卷·A10联盟2022届全国高考第一轮总复习试卷数学(理科)试题(一)2015-2016学年贵州省凯里市一中高二上期末理科数学试卷2015-2016学年贵州省凯里市一中高二上期末文科数学试卷专题03 第一章 复习与检测(知识精讲)-【新教材精创】2019-2020高一数学新教材知识讲学(人教A版必修第一册)-《高中新教材知识讲学》天津市蓟州区擂鼓台中学2019-2020学年高一上学期第一次月考数学试题衔接点16 充分条件与必要条件-2020年【衔接教材·暑假作业】初高中衔接数学(新人教版)(已下线)【新教材精创】1.4+充分条件与必要条件+教学设计(2)-人教A版高中数学必修第一册【新教材精创】2.2+充分条件、必要条件、充要条件+学案-苏教版高中数学必修第一册【新教材精创】2.2+充分条件、必要条件、充要条件+教学设计-苏教版高中数学必修第一册(已下线)第5讲充分条件与必要条件-【新教材】2020新高一同步(初升高)衔接讲义(原卷+解析)(已下线)1.4充分条件与必要条件-2020-2021学年高一数学同步课堂帮帮帮(人教A版2019必修第一册)(已下线)1.4 (分层练)充分条件与必要条件-2021-2022学年高中数学必修第一册课时解读与训练(人教A版2019)(已下线)第一章 集合与常用逻辑用语总结提升与检测-2021-2022学年高一数学考点讲解练(人教A版2019必修第一册)(已下线)1.4 充分条件与必要条件-2021-2022学年高一数学上学期同步课堂习题测试(人教A版2019必修第一册)(已下线)第04讲 充分条件与必要条件-【暑假自学课】(人教A版2019必修第一册)人教A版(2019) 必修第一册 章末检测卷(一) 集合与常用逻辑用语(已下线)专题1.4 充分条件与必要条件-举一反三系列(已下线)1.4.2 充要条件(导学案)-【上好课】新疆维吾尔自治区喀什地区巴楚县2023-2024学年高一上学期9月月考数学试题(已下线)高一上学期期末复习【第一章 集合与常用逻辑用语】拔尖-举一反三系列
8 . 设首项为1的正项数列{an}的前n项和为Sn,数列
的前n项和为Tn,且
,其中p为常数.
(1)求p的值;
(2)求证:数列{an}为等比数列;
(3)证明:“数列an,2xan+1,2yan+2成等差数列,其中x、y均为整数”的充要条件是“x=1,且y=2”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df45047a9d672dd8bc9086f1df20b321.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd8c35ecd3777b7f6379575c5633f1a.png)
(1)求p的值;
(2)求证:数列{an}为等比数列;
(3)证明:“数列an,2xan+1,2yan+2成等差数列,其中x、y均为整数”的充要条件是“x=1,且y=2”.
您最近一年使用:0次
名校
解题方法
9 . 已知抛物线
和圆
,抛物线
的焦点为
.
的圆心到
的准线的距离;
(2)若点
在抛物线
上,且满足
, 过点
作圆
的两条切线,记切点为
,求四边形
的面积的取值范围;
(3)如图,若直线
与抛物线
和圆
依次交于
四点,证明:
的充要条件是“直线
的方程为
”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e52e2eb084820ab6b942145abae0f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d962d9473707de1a8923727d1945259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f464e7ef87c73781f11e78471f19f4e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0753d9770c7fc699de7ee7126ec94ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/605bdf556ed0367721817417cf0bbbfc.png)
(3)如图,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305dc41f7af922a49b3bdfe151776744.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4afec5e278385787e066f099f049fbfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
您最近一年使用:0次
2020-02-29更新
|
646次组卷
|
5卷引用:2020届上海市闵行区高考一模(期末)数学试题
2020届上海市闵行区高考一模(期末)数学试题(已下线)专题19 圆锥曲线 (模拟练)-2沪教版(2020) 一轮复习 堂堂清 第七单元 7.10 直线与圆锥曲线的应用(一)上海市行知中学2022届高三下学期期中数学试题(已下线)高二下期中真题精选(压轴40题专练)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)
解题方法
10 . 如图,在平面直角坐标系
中,已知抛物线
的焦点为
,点
是第一象限内抛物线
上的一点,点
的坐标为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f81a0780efb9c7e876d88a8332a548.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/b4e5a65f-7b27-4271-9de9-b0b898fa845b.png?resizew=159)
(1)若
,求点
的坐标;
(2)若
为等腰直角三角形,且
,求点
的坐标;
(3)弦
经过点
,过弦
上一点
作直线
的垂线,垂足为点
,求证:“直线
与抛物线相切”的一个充要条件是“
为弦
的中点”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f81a0780efb9c7e876d88a8332a548.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/b4e5a65f-7b27-4271-9de9-b0b898fa845b.png?resizew=159)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0011463a8939995c2a498c6b0918c8eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae969dfd9f4fae0fbff6bc4dc02812b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdf60f0d7f4060b1eb05db39438fc519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(3)弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c62d9a936bf146bc7410ebc8f5b1d0cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2020-02-29更新
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698次组卷
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2卷引用:2020届上海市杨浦区高三第一次模拟(期末)数学试题