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解题方法
1 . 设函数
(a,
);
(1)若
,求证:函数
的图像必过定点;
(2)若
,证明:
在区间
上的最大值
;
(3)存在实数a,使得当
时,
恒成立,求实数b的最大值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80027540415bd2b98c9be19e21b5f8d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d285a4c557fc9748105b62ccd94b7859.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b40b1544e62be8b9e9f4dc9f2c0c74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fedf88c1afae37dcb344708fa1918db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09a2b7c019dae83e027830b82b3ee8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2aa311daf7a73f8c45de4462f9d92b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5193a9a29c504059dcbecfb81ca496.png)
(3)存在实数a,使得当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42f54feac6ed738a868ecd53d3a85a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1d9926ad419c75a83ca90457a1e2fc1.png)
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2020-02-10更新
|
256次组卷
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2卷引用:上海市第二中学2017届高三上学期9月初态测试数学试题
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2 . 设
,
,
,…,
,希望证明
,在应用数学归纳法求证上式时,第二步从
到
应添的项是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7d41cdc17d1d73868a0eafb5621a2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f395576519def6a4df88b8fa4e524767.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0598b97e0d061dd458626a080bd1ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8be7b032a433583d2414f9f504b8630.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0ad23f8781ebb49107aa5dbf5fa9fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b00f4eb7f1bd2ccefbabf0c1dfa8f69.png)
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2020-01-30更新
|
234次组卷
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2卷引用:上海市上海外国语大学附属外国语学校2017-2018学年高二上学期期中数学试题
3 . (1)请直接运用任意角的三角比定义证明:
;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75cd397c31481b526bba6136f925b29d.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5417c231457711c7436efc826c66b45a.png)
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4 . 用反证法证明“已知
,求证:
.”时,应假设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cd182ff69c8b9f8c7e6539cf14f148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5977232839b54df456aeeacb13512d.png)
A.![]() | B.![]() | C.![]() ![]() | D.![]() ![]() |
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2018-06-14更新
|
675次组卷
|
10卷引用:上海市徐汇区上海中学2020-2021学年高一上学期期中数学试题
上海市徐汇区上海中学2020-2021学年高一上学期期中数学试题(已下线)第04讲 常用逻辑用语(3大考点)(2)上海市新中高级中学2023-2024学年高一上学期10月月考数学试题上海市南汇中学2023-2024学年高一上学期期中数学试题【全国百强校】河南省南阳市第一中学2017-2018学年高二下学期第四次月考数学(理)试题浙江省宁波市慈溪市六校2018-2019学年高二下学期期中联考数学试题宁夏回族自治区银川一中2019-2020学年高二下学期期中考试数学(理)试题(已下线)广西南宁市银海三美学校2018-2019学年高二3月月考理科数学试题安徽省亳州市第二中学2020-2021学年高二下学期期中理科数学试题广西玉林市市直六所普通高中2021-2022学年高二下学期期中联合质量评价检测数学(理)试题
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5 . 用反证法证明命题①:“已知
,求证:
”时,可假设“
”;命题②:“若
,则
或
”时,可假设“
或
”.以下结论正确的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937559aeec06323cde8861b17024fc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be100015cff38b6dfba5080fa94d128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe44dcfbe7130c760acae3703469dd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2053e1f50472a9fed67d4c84d9cb938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc335ee14fc0b1130900cb82bcb3061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d09b9fc9719ff6faf32254b9d48713.png)
A.①与②的假设都错误 | B.①与②的假设都正确 |
C.①的假设正确,②的假设错误 | D.①的假设错误,②的假设正确 |
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2018-07-12更新
|
760次组卷
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9卷引用:数学(上海B卷)
(已下线)数学(上海B卷)【全国市级联考】福建省三明市2017-2018学年高二下学期期末考试数学(文)试题湖北省咸宁市2018-2019学年高二下学期期末数学(文)试题黑龙江省大庆实验中学2021届高三得分训练(二)数学(理)试题安徽省宣城市郎溪中学2020-2021学年高二下学期第一次月考理科数学试题四川省仁寿第一中学校北校区2020-2021学年高二6月期末数学(文)试题广西河池市九校2020-2021学年高二下学期第二次联考数学(理)试题(已下线)考点43 直接证明与间接证明-备战2022年高考数学(理)一轮复习考点微专题河南省灵宝市第五高级中学2021-2022学年高二下学期第一次月考数学文科试题
6 . ⑴当
时,求证:
;
⑵已知
,
.试证明
至少有一个不小于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03425cbe241074fd29fa5bb2b1da5820.png)
⑵已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39f015b400f6a000a581ef05c9f814ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
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2018-01-20更新
|
1025次组卷
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6卷引用:上海市实验学校2020-2021学年高一上学期期中数学试题
上海市实验学校2020-2021学年高一上学期期中数学试题(已下线)第1章集合与逻辑精讲精练-2020-2021学年高一数学期末考试高分直通车(沪教版2020,必修一)(已下线)1.2反证法(第3课时)上海市南洋模范中学2022-2023学年高一上学期10月月考数学试题上海市曹杨第二中学2023-2024学年高一上学期第一次月考(10月)数学试题江苏省泰州市2017-2018高二第一学期期末考试数学(文科)试题
13-14高三下·上海虹口·阶段练习
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7 . 已知数列
和
满足:
,其中
为实数,
为正整数.
(1)对任意实数
,求证:
不成等比数列;
(2)试判断数列
是否为等比数列,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83d9ea28ccc8c24eeafa2ce1caf71b1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fffd330dd6b9241659d790bd2a7fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fffd330dd6b9241659d790bd2a7fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c14d9ae06f864498048d55088ff4e6.png)
(2)试判断数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b7e7cd571c8cd141cbbfe5d0890bf6.png)
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8 . 已知数列
满足:
,且
,
.
(1)证明:数列
是等比数列,并求数列
的通项公式;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5299d8681e97043a0e449cde0f9731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be9b1d808f2e220696fba4590677ea0f.png)
(1)证明:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b463e643a730e8f11504f135a1400909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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解题方法
9 . 求证:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e01fee1ca9394d318cc7c0fe41418370.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff8eb79da2ae1202feebf45ba5e795c.png)
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2024高一下·上海·专题练习
解题方法
10 . 用
分别表示
的三个内角
所对边的边长,
表示
的外接圆半径.
(1)
,求
的长;
(2)在
中,若
是钝角,求证:
;
(3)给定三个正实数
,其中
,问
满足怎样的关系时,以
为边长,
为外接圆半径的
不存在,存在一个或存在两个(全等的三角形算作同一个)?在
存在的情况下,用
表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fcf8777e54ba6078e0efe810a355b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0be39076f8a9425300e88e60ee9052.png)
(3)给定三个正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aadb354aceba145fa22173f87a00488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c659396f6a0f72e213185b1ab2e198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aadb354aceba145fa22173f87a00488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15bd315b801f71bc30b8d772098614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aadb354aceba145fa22173f87a00488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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