如图,在矩形
中,
,点
是线段
的中点,点
分别为线段
上的一点,且
,点
是线段
的中点.
的值;
(2)若
,求线段
的长度;
(3)设
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fea5ae69e4210b126a9b17fc761182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a8f3a13cb258c61e2a221c2bf09979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30196bc4b03a72c9b059e81eccb83240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c40f07ccddb4743a1890e73b6a259d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a077b3ecaa766e440b5ab3c88c654ef6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de809f456d944a402d2ff017131e962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e04bb23709542d0388b8d514cb24b673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7521a633649628851249dd0cf6f2ff6.png)
更新时间:2024-05-22 21:30:52
|
相似题推荐
解答题-问答题
|
较难
(0.4)
名校
解题方法
【推荐1】已知函数
,
,且
在
上单调递增.
(1)若
恒成立,求
的值;
(2)在(1)的条件下,若当
时,总有
使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ffc29095607e86d6cd2f55a79e7193.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d91a4ab67a4edb4b62f4e36ea89035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3aae9c8988f4a48db69cad3308942c9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98d3196f675600803cdc74c72470d32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
(2)在(1)的条件下,若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4361b7baf57ec27b60ac4aa637e16a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00fff2634ce3999c544b19d011924df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e63bbadc6250f7139836ede33205550.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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【推荐2】如图,已知直线
,
是
,
之间的一个定点,且点
到
,
的距离分别为1,2,
是直线
上的一个动点,作
,且使
与直线
交于点
.设
,
的面积为
.
的最小值;
(2)已知
,
,若对任意的
,不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027830fc47290062692964077ee481e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c499d3ef329f85e59fd72dec6f453bbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0496f7b645615d6cf59b8a7ec1fb6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c0496f7b645615d6cf59b8a7ec1fb6e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcd9218a657b17654c5d757a6f7dee9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4387e0bcdeae4ff80549beb1c5ef7ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcbe8b4bcd32e5a64ebfd873f8cbb2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e1cfcf2f6f715c0e8384582947268c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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【推荐1】已知向量
,
.设函数
,
.
(1)当
时,方程
有两个不等的实根,求
的取值范围;
(2)若方程
在
上的解为
,
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572fc5c87541aecef5415a615f1bada5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b8869f9175eba34e6743a18d3e32d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8a1c7bb5733da5eebbf2b3d8ea0a92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b392ae979e54da7e26bbc2d967a72666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c99a65cb87c5b4d050b5c0cc66dff4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87d3225dc94f540306b55c70d600744d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ff8dca35b759d3051b62badd7d76bc.png)
![](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/e058eeb9cea0d93756125087c6655325.png)
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【推荐2】在
中,角A,B,C所对的边分别为a,b,c,请从下列条件中选择一个条件作答:(注:如果选择多个条件分别作答,则按第一个解答计分.)
①
②
③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd161755aa7f1e0c4313a2327cb7e7b.png)
(1)求A的大小
(2)若
为锐角三角形,求
的取值范围;
(3)若
,点A,B,C分别在等边
的边DE,EF,FD上(不含端点),若
面积的最大值为
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb639420971554d620202a8880357f3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c390057bfe42a58d0cfd4c33f095d287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd161755aa7f1e0c4313a2327cb7e7b.png)
(1)求A的大小
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99ea513ef4c8fc4d8c31eff498740680.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5742b2684d00be50a66e01c9acb6b51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e56e21a9e25f762fbf4b1a143b128aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
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【推荐1】蜀绣又名“川绣”,与苏绣,湘绣,粤绣齐名,为中国四大名绣之一,蜀绣以其明丽清秀的色彩和精湛细腻的针法形成了自身的独特的韵味,丰富程度居四大名绣之首.1915年,蜀绣在国际巴拿马赛中荣获巴拿马国际金奖,在绣品中有一类具有特殊比例的手巾呈如图所示的三角形状,点D为边BC上靠近B点的三等分点,
,
.
,求三角形手巾的面积;
(2)当
取最小值时,请帮设计师计算BD的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a58a622e2b1a239f2f96aa1501e9799.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2bdcd23d2c26d9df0b4756d8a715673.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746853ea6d76bd7cccc6bdd6c739aed7.png)
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【推荐2】在△ABC中,内角A,B,C的对边分别是
,向量
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059092be2537c92c6eeb9dae1ec73efc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fda47b6d741e5a832a639d64d97dd91f.png)
(1)求角B的值;
(2)若,且
,求△ABC的面积.
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【推荐1】在
中,
为直角,
,
,
与
相交于点
,
,
.
(1)试用
、
表示向量
;
(2)在线段
上取一点
,在线段
上取一点
,使得直线
过
,设
,
,求
的值;
(3)若
,过
作线段
,使得
为
的中点,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2981bf2261343f905ec1b5355a3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d7b2fe01a33c4825f9974ed9663a99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c607be8fbe8b2701e0451e9322223e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca7757b00ff2bdc8796ccfa33fec0293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6942bd9fc5d090de0cfad7022aa32f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cc63e33fe47da2704cff57d148dde0.png)
(1)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00da1c29aea46e36cda0f5780966bb6.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f9c6f622be010cd1d9cc5c13f4fd9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23438690dec68d60e07d2ab6bdbf1d34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9ebeb198e80f9c2e6406f0601554b92.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228f00eb81c06f6862e15e923109c35b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2d713292dd1f9f367d382077c703d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df3b182fcad057f49f2360d6d2b4dddf.png)
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【推荐2】对于一组向量
,(
且
),令
,如果存在
,使得
,那么称
是该向量组的“长向量”.
(1)设
,
且
,若
是向量组
的“长向量”,求实数
的取值范围;
(2)若
且
,向量组
是否存在“长向量
”?若存在,求出正整数
;若不存在,请说明理由;
(3)已知
均是向量组
的“长向量”,其中
,
.设在平面直角坐标系中有一点列
满足,
为坐标原点,
为
的位置向量的终点,且
与
关于点
对称,
与
(
且
)关于点
对称,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77f81d9f99e641bb157713fdeedc259f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92c1d22f02fa7f8f1ff1db3f322a9fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e955b4525bb55e72c131d829406df508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c98c622975aaf93ed0c63be1294d2170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f50ecfa147131019f969c3bc78169f7.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c33a899454f0d42377d4ea0324dd812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67dbe2e19d8960789ec873b687998b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0aca31150d49fff8a60dc4d5df88a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c75496cf010597a274404439722ba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa63e77491c081392e287e60b507da8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd2c185dfb8bccce40ca2818c652cd99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0aca31150d49fff8a60dc4d5df88a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0aca31150d49fff8a60dc4d5df88a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45647cbdf82e8c6a1fe3ea5f79d760dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280cf6971687fe4fc518d29f24c40709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e47e7afd7287b26737db83b5e709a881.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82dc7540c4cdee4c34a9311c79b35d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc4dc226800792c55eaa32134041837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f306a75051c9a11c92aa30a836a016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b5ea93b62e9b06f0060ab0d09e6633.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc4dc226800792c55eaa32134041837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e10f2f74e201f77f853e9ed9078615c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
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解答题-问答题
|
较难
(0.4)
名校
【推荐3】在锐角
中,角
所对的边分别是
.已知
,
.
(1)求角
;
(2)若
是
内的一动点,且满足
,则
是否存在最大值?若存在,请求出最大值及取最大值的条件;若不存在,请说明理由;
(3)若
是
中
上的一点,且满足
,求
的取值范围.
![](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/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a64962ad7ac80b078a676e70bad4ce6e.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b70494b72a951263128f2961992b9c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136cdd691e63a13b934567ddd7642d85.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8245244d6c3a1e703fb7f658defd8277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a732126df5fa76243880cc9e10cc97fd.png)
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