名校
解题方法
1 . 已知
,
,且
,证明:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7dbc702617c765a573961953cc0901.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ba449a8e384c9696b21ec11f19e256.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef22557e767d36c91571675e964825e4.png)
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2022高一上·全国·专题练习
解题方法
2 .
,
,
,
,设
,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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a3aeebf26c15b9f3682341681fac26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96bde2d960c74c094cafd27a98eb91fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57872d61b27a7e370e9fe2a62652490d.png)
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3 . 已知数集![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
具有性质P:对任意的k
,
,使得
成立.
(1)分别判断数集
与
是否具有性质P,并说明理由;
(2)若
,求A中所有元素的和的最小值并写出取得最小值时所有符合条件的集合A;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40dc6d234f7984333f33d89de05e7ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110ef251c0b9cf48fb94c928ad95e36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412f8627babba57acd06ed10f4292210.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1e76d1341e8e6bd89b7075150536bd.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997bbd93dff19a5dba79bcd9d92f3129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13470c4e9665748fdd20d0b181abc8e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91a94ec87afbc073e077f2c453a304b.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e73d1fc9adb4448fd245f9bbf3d3ed0.png)
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名校
4 . 基本不等式是高中数学的重要内容之一,我们可以应用其解决数学中的最值问题.
(1)已知
,
R,证明
;
(2)已知
,
,
,
R,证明
,并指出等号成立的条件;
(3)已知
,
,
,
,证明:
,并指出等号成立的条件.
(4)应用(2)(3)两个结论解决以下两个问题:
①已知
,证明:
;
②已知
,
,且
,求
的最小值.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1f5facca1d0db44613d7c690bc90aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267cd7062303bbe8d8a4bd8dd48fef2e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7701d084d2b153bbea08cfbf63413a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f61d582437402db050313612348dfa27.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d51126fd77ba262607809563550b48f.png)
(4)应用(2)(3)两个结论解决以下两个问题:
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5acd1467c10c7ff14caca53feea7a540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d49468bf449d201b533f5f8f9e9add1.png)
②已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983154ee44321cef8eb8213bd862c70d.png)
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2024-02-10更新
|
121次组卷
|
2卷引用:云南省昆明市官渡区第五中学2023-2024学年高一上学期期中测试数学试卷
5 . 正项数列
满足
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85dcdd36191a256bc058ada311209fb3.png)
(1)求数列
的通项公式;
(2)
,
时,
①证明:
;
②证明:
.
![](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/85dcdd36191a256bc058ada311209fb3.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
①证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c404d276cdabdb544091df37f3cfb292.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/242a27a7a522c6461753218cac3d0066.png)
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2024·全国·模拟预测
6 . 已知
.证明:
(1)当
时,
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b8b32dd4e8910769e4176362d7b40b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e84dbb03e8c627ff11d5c7aeb0c8b5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7ad23e894950eb21a3da9f40433e6f.png)
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名校
解题方法
7 . 设
,
,
.
(1)证明:
;
(2)若
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baca30d4248a82988890bd032d159b25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56667aabbe787eb1c3189d487d203e22.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9788f8969e6699384d73cd782ac1184.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/432d77fe5ad3032d59a237dd94c8a638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2128a00f52af4427721f0ebba591daa.png)
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8 . 已知函数
(其中
),且
,
.
(1)求
,
的值;
(2)求
的单调区间;
(3)若正实数
,
满足
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64527c19df5c1d45128d4d26c4a886be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6455e38ff53ede2508e4d9cb23f0b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e1d97c42f236c05bd0f97ee6538ea61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b49cf13331c53446d9082db8734157.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(3)若正实数
![](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/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d900314efb0e4cacb6e5de945b5397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ca3ecbbaca8eeb1cfa8f4035f7d5726.png)
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9 . 已知
.
(1)通过二分法且满足精确度为0.5,求方程
的近似解(精确到0.1)
(2)设
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d4ebe573c27995ad5bfb45fbda2348.png)
(1)通过二分法且满足精确度为0.5,求方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b92b70365c63607daecdc8deb73ecf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d763f75099726be470cbb078e04a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c4cff161f2c07165b8117f4c22e43c.png)
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10 . 证明下列不等式
(1)已知
,
,
,且
,求证:
.
(2)已知
,
,
,求证:
.
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
(2)已知
![](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/4cad3aaeb5b444feb152378278f68863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5cc7582a7b091b3f0f5a51325e1d0a1.png)
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