1 . 求证:数列
中一定有2022的倍数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69719252d1232ef3ce59579f51104c81.png)
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2 . 若一个直角三角形中两条直角边都是整数,且周长是面积的整数倍,则称其为“
三角形”,则这样的“
三角形”共有______ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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3 . 已知
,则
的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e8cbd2870d3b6372609f82c491a803.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c69601415aff5dd2d9fee2ba26f81c.png)
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4 . 设正项等比数列
满足
,
.令
求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28ef6f1b2279af482557a8ea46f2e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/853eace02560e7f1490694276c29a856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/057f84c7e6b5cfde2e11dd1926c50790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412d3d040e4e67daad25aa085fc45e0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/783af6a1ae35709a95b4287409348310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da2db7e09d2b1dbfbcd02574dae25ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b143f8888579b22c2fe7e70516310a.png)
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5 . 在平面直角坐标系中,抛物线
:
的焦点为
,直线
交C于A,B两点,延长AF,BF分别交抛物线于M,N两点.令
,
,
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91356fe1338cd458e4b1761b36873145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b6a742dbacdab5aaa298007663dd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91703f114468effe42cc90bfbcaccc94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cfc1cf121adab4cddcdd98415b3a3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22b8cc74825d62042a387df3ca6542ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7faa87c58d6807e27193ab43be29e86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11d75bfbd8b05a5987d579f35b2969a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fa605fe0907e944ec0f716cad93002.png)
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6 . 在三棱锥
中,
,
,
,
.若
和
都是等腰直角三角形,则满足条件的有序实数对
的个数为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e43f6eb62e48e72e06361138e0d1e4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40381b7c837e66aeb112843d52b6e3ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b3b0b82a9522b525a636bc65c92868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c4a5c82b0044673d554169f8529be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2534555d85b44a6fe84ec8a18ad3583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ad1c5f04609e8c1231c7f246662a165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0be1ec33951eb3e12fa523e3ebb3a954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8b1eb1dabc7725dea6fa617f9fd103.png)
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7 . 设
,
满足
,
的最大值为3,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/527736d1f97648cfd189cf086f4d48dc.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd03181a10a2889263499aec1313d0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0c3187c16fa72cdeb875a8a8e1711a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b592b8a60d03aad90e12ab79bf4a2649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449e3c61cc51f06c5c0175dcb9921311.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/527736d1f97648cfd189cf086f4d48dc.png)
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8 . 已知
,求最大的实数
,使得对任意大于2022的正整数
及实数
,存在集合
的一个子集
满足
对所有
恒成立且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3c5cb4d381a7d02ed31e3d92ce4306e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a425978da20cebf8c4c63953579e7b35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c6971463b9839ecc1c2352ae0afb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0478ec4c7dcce9fa624789a6223eb53d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44c4dce884147e801b50675b9c0714e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e64c35495f9f68ad197ba30902915c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d81314852212a08f2e6d36338d0368a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0a9f3aaedf6f256f10159eaf262a5b.png)
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9 . 已知
,若
,
,
是函数
的零点且
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cadb751863093633424831bbd30bb39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12a4eecd249473a831d0ee472470240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9565876bc50bceb63e5793c8c67a9032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ec13d0c7a2f811a742d7e89960c5fec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a31aaa7bcac98bcfc3591261792232d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8567c0348e755bc0542cac37f3522d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ef98c71145edae104c6c03d8e91ab50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04127db1410188b8076c89b79dccfe0f.png)
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10 . 设
为整数,
为实数.证明:存在整数
,使得对于任意实数
,均有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abefc7e7354cd2d17283c16c494ea879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5040ce82e687fd1a6f48442f36975523.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821ce7a655e8b5fecb99e04313c700b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f97bc1796c160ab600db7d85287ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e137ac7b96922341e43887e7f5fed30.png)
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