1 . 已知定义在
上的连续函数
满足:
①
在
上单调 ②![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c448ed9d5ca0d0f84cf007684b08f10.png)
③
对
恒成立 ④
对
恒成立
若
,
,
,
,记
与
形成的封闭图形的面积为
,
,则满足
的最小的n的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2aa311daf7a73f8c45de4462f9d92b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bffc9c4bf9de4d804885955aff039ca.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bffc9c4bf9de4d804885955aff039ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c448ed9d5ca0d0f84cf007684b08f10.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38240e7724899d20a03013ef766b415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24aa16b780156e18f12baa2b8ee0f9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77e0a3c0331e0835b3cb737fc2d1abe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790daaa89fc9d093f45023becf765697.png)
若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5174aacbaeb543de8b00404aaa088bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce34fa4f5cb60847d6b5bbdfb29ccfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac69e6db1df13ed64756b4f391ae9fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d68596c56739bd1bbe14c675804cfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12ee0b997df5dddf6c32c106d47196af.png)
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2023-07-05更新
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4卷引用:吉林省长春博硕学校2023-2024学年高三上学期期初考试数学试题
名校
2 . 圆锥曲线具有丰富的光学性质,从椭圆的一个集点发出的光线,经过椭圆反射后,反射光线过椭圆的另一个焦点.如图,胶片电影放映机的聚光灯有一个反射镜.它的形状是旋转椭圆.为了使影片门(电影胶片通过的地方)处获得最强的光线,灯丝
,与影片门
应位于椭圆的两个焦点处.已知椭圆
:
,椭圆的左右焦点分别为
,
,一束光线从
发出,射向椭圆位于第一象限上的Р点后反射光线经过点
,且
,则
的角平分线所在直线方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54058d8ebebd0449a3f6a6bb8358ce3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/8bacf061-6f55-4ce7-8299-8520fab50df4.png?resizew=325)
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4卷引用:吉林省通化市梅河口市第五中学2022-2023学年高二下学期期初考试数学试题
3 . 平面上到两条相交直线的距离之和为常数的点的轨迹为平行四边形,其中这两条相交直线是该平行四边形对角线所在的直线,若平面上到两条直线
,
的距离之和为2的点P的轨迹为曲线
,则曲线
围成的图形面积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42498f6e0fc9a61c9857b70a87f02c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a7df955fc17e92fd86302f8c34664a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
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解题方法
4 . 圆
及
围成的平面阴影部分区域如图所示,向正方形
中随机投入一个质点,则质点落在阴影部分区域的概率为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6316e0e6da742e9b035d8f2cc91a4dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e265ce107592c375b78007107a9c00a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea16ceca816f7d3d50650af141baf42.png)
![](https://img.xkw.com/dksih/QBM/2021/5/2/2712442821754880/2712925142007808/STEM/14786c84-ae3a-455e-85d2-c16291220eaa.png)
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5卷引用:吉林省林实验中学2021-2022学年高三上学期开学测试数学(文)试题