解题方法
1 . 平面向量
,若存在整数
使
,且
,试求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a4521f0658e021ad28318d8db27426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09737e117adb481fd3c4affdf38ff45f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/245d4ac7e6c91f3ea4028bdeb2fb1a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f92ffd4c85efa2d4a1692459a06cbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bdb686910f213670f2c6f9e46c1f62.png)
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解题方法
2 . 已知
(其中a,b为常数,且
)在
上的最大值和最小值分别为
和
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200dd30171e6c5895abbda91d0e9d195.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b172723002461ae60798317e2f10f6c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f190b17530d81d927c358ac84757a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
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解题方法
3 . 在
中,已知
,以A为中点作长为2a的线段PQ,当
的值最大时,
与
的夹角![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc130e4f2499cc620a0df6542d8127b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c1954674261703d6c846f956520e90b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bad299e2782c072d27e1c54422cc8fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89265cbe3abc6b966ce8967fead448b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b657cfa91b6394e4b00fa385a2c0149.png)
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解题方法
4 . 直角坐标系中,曲线
围成的图形的面积是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b4be8be0a986e703df7b0dc3f3401c.png)
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5 . 设向量
.
(1)若
,求
的值;
(2)求
的最小值;
(3)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0510ef1fb0c12cfaaa6de62c479f045d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f17e09caa19b707485eeb63c03d4b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fee7e2969987222954a10a03d200c03.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2defd5a8aae63078a68baf77071d37.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f7d08d10754ff3903d139768f40530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58f04d44d8e08c76a9f5bc24413cf49b.png)
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6 . 为使
在区间
上至少出现100次最大值,则
的最小值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce08482e06228af09c74c6f8026fa1f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.198 | B.199 | C.200 | D.201 |
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7 . 已知向量
不共线,且实数
满足
,则
的值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10814bc3db929e79874befe96cf4e3d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2ca2047184f3edda733ce3123082cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a1c81bf870a55b94f0640318f59118.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 已知奇函数
的定义域为
,且为
上的增函数,
.
(1)求不等式
的解集;
(2)设函数
,
为锐角,求满足条件
的
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a28068770a85b88b42321cd71ecd3c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3471484b64504fc545398f52be830010.png)
(1)求不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b666663ce3537a634a3b427b418eb62.png)
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e391cf5a502f173dabb76b2a3abbe0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316d0f0ccbff34b8d6727afba7eeef49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
9 . 已知
,
,且存在实数
和
,使得
,
,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9798750055cc3be811b36accdec975d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28e135eb6709b5d964f89ce0e391062a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4749a22a7ae411cf646c64fdbf08e1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f4b8e9bf365f34a58866b4fdf2096e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654c8d7389fbd7fffd7e00071f814016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a17fbeeb7bc8ff39e2b0403042f026.png)
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10 . 对平面直角坐标系
,保持
轴不变,将
轴绕原点顺时针旋转
后形成的新坐标系
称为
斜坐标系.原平面内任意一点
,经过上述变化后在
斜坐标系的对应点为
.对于如图所示的
,设点
在
斜坐标系中的对应点分别为点
.已知线段
上存在一点
,分
所成的比为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/4c7edd10-77ac-4396-9d2b-570a96148545.png?resizew=169)
(1)求
的面积;
(2)已知
,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](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/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8bc439c8dd910f1ce5aac8cdcad942b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98226d9d5a14f9572a862e62b5c6aee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c5b9d864b406b04cdbaf4e8972e4eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecb94640ab11447c26a9c4f272ba192d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/4c7edd10-77ac-4396-9d2b-570a96148545.png?resizew=169)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8ee6e1d480ece7117e1f87ebf4bbeea.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9fcf44e5f105d71562ad54cc6a4b83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/975fc183ba81c67cba79a2b2567907ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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