解题方法
1 . 已知
,给出下列四个命题:
:
,
:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a92956b1693c71902b15e45118c1f87f.png)
:
,
:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac624f921a4282e16b160384c47414d0.png)
其中真命题的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9994c0aefa7220691dbcb9afa568a182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9309362eb34cd9d0d5757836f8d2fc55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e686113ca2f873c4a911c8c636a39f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9309362eb34cd9d0d5757836f8d2fc55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a92956b1693c71902b15e45118c1f87f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0c5a96a4f87442cbfc05e59de281ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e3bf4d705125cab1f1868283ffc900f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c0c5a96a4f87442cbfc05e59de281ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac624f921a4282e16b160384c47414d0.png)
其中真命题的是( ).
A.![]() ![]() | B.![]() ![]() | C.![]() ![]() | D.![]() ![]() |
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解题方法
2 . 在
中,已知
,若
最长的边长为
,则最短的边长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c44ca2c5d2835f2555d31a77a8146fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4056761b8f826eeb6ad8c9a151d3c9c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 已知集合
,设
是等差数列
的前
项和,若
的任意一项
,且首项
是
中的最大值,
.
(1)求数列
的通项公式;
(2)若数列
满足
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a101d7fe85109e613e4fdff218e32f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](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/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6302fc3e3d1fac960e84950c0e814a19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdbfa7a63fdf5717d40c8c9a73ec160.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b18378ba893f1ce0814c9582699ae29.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166e346727bcaf56431b36ef42594af6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b511d10eb2d2d913d7282778206db331.png)
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4 . 在锐角
中,角
所对的边分别为
,且
.
(1)求证:
;
(2)若
,求
的最小值.
![](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/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73871b5eba746c60026c5cce7482d66f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8636e448103248ddd367d084be0ef715.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c03b5fd68e38254b1e0a9bcd5401c38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64da75a02173c2a5eb40f4c68d0f4f36.png)
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解题方法
5 . 在数列
中,
,若数列
是以3为公比的等比数列,则
( )
![](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/636a4c1710469f090d45f77976d16a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/175b4855b799d276f733969aa6b34d4b.png)
A.1006 | B.1007 | C.1008 | D.1009 |
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解题方法
6 . 已知a,b,c是的三边,若满足
,即
,
为直角三角形.类比此结论:若满足
时,
的形状为( ).
A.锐角三角形 | B.直角三角形 | C.钝角三角形 | D.以上都有可能 |
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解题方法
7 . 已知圆心在
轴正半轴上的一系列相外切的圆的圆心的坐标为
,且满足
,第
个圆的圆心横坐标为
,这
个圆的面积之比为
,记
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a19af21827ffd49c3842e1443244940e.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e684bbf8039dc14ea6a402f3478b3aa4.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/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/702de74c38885954ec1fff041b0c2f03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3f933f2a8c0a6a2a2903a071c18c9db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a19af21827ffd49c3842e1443244940e.png)
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解题方法
8 . 对于数列
,定义
为
的“优值”,已知某数列
的“优值”为
,记数列
的前n项和为
,若
对任意的n恒成立,则实数k的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970b408e394a469cf86916e899e1ed80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d935e25db28c6ec9b7ae700cd335edbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071c744a45fd2d97a3e616a04495ff6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3523a941f4af78066c6f587e8d001df0.png)
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解题方法
9 . 已知
中,
,且
是
的中点.
(1)求
的长;
(2)点
是以
为圆心角的劣弧
上任意一点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d693502347914315f74cc56b59ed67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb8eca20ce2c918ea4034ea15210c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f9353ca110c8b81561455b232dbc15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82888987e0057b5d54f0d9f85a318f5.png)
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10 . 已知数列
各项均为正整数,对于
有:
.若
是不为1的奇数,且
恒为常数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bca4120bf19e50a650695122b2ac74ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f7fda69e2b32b9ced2239f915fa59b.png)
您最近一年使用:0次