2023高三·全国·专题练习
解题方法
1 . 正实数
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5b65fc56819e868e67b1ed350b4e85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bcf5b014aa4e0345d9c4f65590c682.png)
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2023高三·全国·专题练习
2 . 正实数
满足
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331c7a460306e9d4a96409eb81444ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/768ca5be31bb4a89278e4e026d25f71b.png)
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2023高三·全国·专题练习
3 . 已知函数
,当
时,设
的最大值为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61d7fd7b50dd0338005c76689c7a67fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69303621c56f67b4ec4e0ac575deb554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d6bb01f1044358cc5fee441bc62489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d6bb01f1044358cc5fee441bc62489.png)
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2023高三·全国·专题练习
4 . 设正实数
满足
.证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751e274e9107d780c39ba9c49d6daefb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceb22dc52f06323a43671194cee5b7dc.png)
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2023高三·全国·专题练习
解题方法
5 . 证明:圆的所有外切n边形中,以正n边形的周长为最小.
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解题方法
6 . 已知数列
的前
项和为
,数列
满足
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da79ef177d409befa3f383d8bccf5202.png)
(1)求数列
的通项公式;
(2)求数列
的通项公式;
(3)对于
,试比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35768aa9802e264582c4ca649b1296d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da79ef177d409befa3f383d8bccf5202.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
(3)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28652e52c0b02a343e618935ea625cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95931effbd59c43e8ed1ea09962b84f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
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22-23高三下·上海浦东新·阶段练习
名校
解题方法
7 . 定义在R上的函数
,若
对任意的
成立,则称函数
是函数
的“从属函数”.
(1)若函数
是函数
的“从属函数”且
是偶函数,求证:
是偶函数;
(2)若
,求证:当
时,函数
是函数
的“从属函数”;
(3)设定义在R上的函数
与
,它们的图像各是一条连续的曲线,且函数
是函数
的“从属函数”.设
:“函数
在R上是严格增函数或严格减函数”;
:“函数
在R上为严格增函数或严格减函数”,试判断
是
的什么条件?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18320524896150a2d5cd223c6eb46182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec6c7a1da7ecaef51a3d08fbcdf2821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fd423a80d5b6fea8753fa1813cfbcc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.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/6a1cfb60420ff7e72c1b9d64f69ae063.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b33f268478cd00d6b3402377f8deff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10ede78fd7ac619ea597856254bb5d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(3)设定义在R上的函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
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解题方法
8 . 已知数列
中
,其前
项和记为
,且满足
.
(1)求数列
的通项公式;
(2)设无穷数列
,
,…
,…对任意自然数
和
,不等式
均成立,证明:数列
是等差数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f085575b5c456ae641143d2d430458b0.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7121ac4377ec9bcd071cb259678ab071.png)
(2)设无穷数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/402b8223a5be456f2acb45f65648eb34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fce83115a50f99e08e9a2db7267aeed.png)
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名校
解题方法
9 . 已知
,求证:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a00faa512fd8f8d7209830cb72fb5d1.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eaa7c8f30d13101eddedb31ae84d499.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/088668e33525e79abf7d1d6dad4b5be9.png)
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名校
解题方法
10 . 已知函数
.
(1)若
,
恒成立,求实数
的取值范围;
(2)若
的最小值为5,且正数a,b,c满足
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93601c572ce6fc8e40f5e748c42a17f9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96b743603ab1c10330622f16db78dbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369100ccd44feaa77e5f119ea949a879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91beeecb519bfc3c9afbd86f0537e589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aae622f238d45382a3a386ee1f83022.png)
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