1 . (1)求证:
;
(2)已知在
中,
是
的中点,证明:
;
(3)已知
,
,且
与
不共线,当
为何值时,向量
与
互相垂直?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2052b9d309f07cf3b9544f09a2223b71.png)
(2)已知在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e1a5884f5abdf9d72561b7a591eda65.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6316d995f00623f05fc3d56a6cbe5f00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407538138dd68ab917925c2063cc98e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9441846da0868582298cece138bec3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff01c3e3b53271c5d16ad4e02a930ad.png)
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名校
解题方法
2 . 已知定义在
上的函数
满足
,且当
时,
.
(1)求
的值,并证明
为奇函数;
(2)求证
在
上是增函数;
(3)若
,解关于
的不等式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc2ae509aed37fd2e2c8faa640ab231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c3f4162ae5563b2c9737d0979b1926.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e38fffbc7ab9882480f4faa72390e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d43e46dba47f1543056c1e376e16ab.png)
(2)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933093b52cca887f597cbe22a5467b11.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ed670b1f668778c6243f3f7470ee7d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9521a6482b63d10996088eec2c7f1083.png)
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2023-10-12更新
|
2008次组卷
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4卷引用:河南省信阳市2023-2024学年高一上学期期中数学试题
名校
解题方法
3 . (1)已知
,
,
,求证:
.
(2)用分析法证明:对于任意
时,有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf913c92060a7bad4de1ee8c04d011e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9f2a4ec61fdebbfc77f04e789ea7ed.png)
(2)用分析法证明:对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6964979a90a2036e9dd541c40cb50be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e8010392b125fb5f015992bad5d6fa.png)
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2022-04-20更新
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185次组卷
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2卷引用:河南省郑州市十校2021-2022学年高二下学期期中联考理科数学试题
4 . 设数列
满足
,
.
(1)证明数列
为等比数列,并求数列
的通项公式;
(2)若
,
,
.求证:数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13a6e1d671215fc96e4bee3541d1096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b973cef9460d84bec30961a9d3443cd.png)
(1)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d483eb4433fee05a5810a276433b1742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e1ee88beaddafb0d0a185c3a8e0dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c35bcffef993be362ae7652c505c60f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de2dfb798d7a257f815574af575dc1cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee920027400a94a0e37ed32de8c4f114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f63b998f4909841e47575281936b3f55.png)
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2021-11-16更新
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481次组卷
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2卷引用:河南省南阳市2021-2022学年高二上学期期中考试数学试题
5 . (1)设
,
,
,求证三个数
,
,
中至少有一个不小于2;
(2)已知
,用分析法证明:
.
![](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/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e911b4c3316981231030c185079161.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a63422d35f6c4476e6bdcb4b95f092c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fd1759f63c9d61781cdfaa8e3a735d.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/055365d21f92fdb6881310bda08c3f75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700b662f55194073cc8cc44e9c002d59.png)
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2021-08-13更新
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310次组卷
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3卷引用:河南省洛阳市2020-2021学年高二下学期期中考试数学(文科)试题
名校
6 . 按要求证明下列命题:
(1)(用分析法证明)已知:
是不相等的正数,求证:
;
(2)(用数学归纳法证明)
(
).
(1)(用分析法证明)已知:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98941347dd7ac01f5e63a6c5930dd5fa.png)
(2)(用数学归纳法证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b256115e3b54ef332792fa167cc43bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea4ac187cbb465180e89f38250b3970.png)
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2021-09-03更新
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146次组卷
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3卷引用:河南省实验中学2021-2022学年高二(下)期中数学(理科)试题
河南省实验中学2021-2022学年高二(下)期中数学(理科)试题陕西省宝鸡市金台区2020-2021学年高二下学期期中理科数学试题(已下线)4.4 数学归纳法(课堂培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)
7 . 下面是由大小相同的小正三角形按一定规律所拼成的几个图案,其中第1个图有1个小正三角形,第2个图有4个小正三角形,第3个图有9个小正三角形,按此规律,用
表示第
个图的小正三角形个数.
![](https://img.xkw.com/dksih/QBM/2021/5/5/2714412955836416/2784563175645184/STEM/67e863780af64409b59297b7e13848d2.png?resizew=326)
(1)试写出
,
的值;
(2)猜想出
的表达式(不要求证明);
(3)证明:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/2021/5/5/2714412955836416/2784563175645184/STEM/67e863780af64409b59297b7e13848d2.png?resizew=326)
(1)试写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32a859898e9905e0524d3a982eb34b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3627e4ccde7d69c49034a4a2d10bee5.png)
(2)猜想出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a90e59aea1ddbfdc83161a47874eff.png)
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2021-08-12更新
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182次组卷
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2卷引用:河南省焦作市2020-2021学年高二下学期期中数学试题
8 . (1)设
,用综合法证明:
.
(2)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ada798eeba5bd19d497bfd0741afd00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1caa2030ac2f57deccc5b24e940facc9.png)
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2021-04-02更新
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3卷引用:河南省南阳市2021-2022学年高二下学期期中质量评估数学(理)试题
名校
解题方法
9 . 已知函数
对任意
,总有
,且当
时,
,
,
(Ⅰ)求证:函数
是奇函数;
(Ⅱ)利用函数的单调性定义证明,
在
上的单调递减;
(Ⅲ)若不等式
对于任意的
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941b4ceaf8c97a676d9ad3320cb940d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf72bb8497a21b03e0ebfc1faec3079d.png)
(Ⅰ)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(Ⅱ)利用函数的单调性定义证明,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(Ⅲ)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d13a6fbeec8019554bfe254504ed41ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00231660ef092b9383a4d4196c8ef850.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2020-11-26更新
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731次组卷
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7卷引用:河南省驻马店市上蔡县衡水实验中学2022-2023学年高一上学期期中数学试题
河南省驻马店市上蔡县衡水实验中学2022-2023学年高一上学期期中数学试题北京景山学校远洋分校2020—2021学年高一上学期数学学科期中测试试题湖南省长沙市望城区金海学校2021-2022学年高一上学期期中数学试题河南省鹤壁市浚县第一中学2022-2023学年高一上学期10月月考数学试题福建省厦门市湖滨中学2023-2024学年高一上学期期中数学试题(已下线)练习11+抽象函数性质专题专题-2020-2021学年【补习教材·寒假作业】高一数学(北师大版)(已下线)3.2.2 奇偶性(精讲)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第一册)
名校
解题方法
10 . (1)已知
,求证:
;
(2)若x,y都是正实数,且
,用反证法证明:
与
中至少有一个成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ada798eeba5bd19d497bfd0741afd00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbc2278547879e9246de7e749a774d7.png)
(2)若x,y都是正实数,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9e131cdd242d56b6dba05ab3363ef3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36ffaf917dcebc8719f2ca539a774ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8e5b510c343f9d3d626fa1a4b36bad.png)
您最近一年使用:0次
2020-06-16更新
|
394次组卷
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4卷引用:河南省洛阳市2019-2020学年高二下学期期中考试数学 (文)试题