1 . 已知关于
的不等式
对任意
恒成立,则实数
的取值范围是___________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af34fa130c976150970d9da1bb21b56f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95ab6ce2369fa5338d1fa5589bfbc96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 已知抛物线
的焦点为F,过F的直线l与C交于A,B两点.过A作C的切线m及平行于x轴的直线
,过F作平行于m的直线交
于M,过B作C的切线n及平行于x轴的直线
,过F作平行于n的直线交
于N.若
,则点A的横坐标为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7093538ecfb10a639b23863e7331a66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7093538ecfb10a639b23863e7331a66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3063f30032fb92e774ca2129480c840b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3063f30032fb92e774ca2129480c840b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c737d2396f60974f6128d4d47cf93940.png)
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3 . 若圆C与抛物线
在公共点B处有相同的切线,且C与y轴切于
的焦点A,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1d7cc83e49b858c7771754fbc83ea0.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e5cab50c76f67a62a75cfe02f08f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1d7cc83e49b858c7771754fbc83ea0.png)
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名校
解题方法
4 . 已知函数
,设曲线
在点
处切线的斜率为
,若
均不相等,且
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131162cc07da30aaff25ee2146086547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e61a4b9858f8f8132718ebe85d59c3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369cea49a817363ca35a476927853b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c328ce481f74b1a2ff07f295ae36a5d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62bbe3c8844c1e329350b42913248f5.png)
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2024-02-29更新
|
3302次组卷
|
7卷引用:广东省深圳市2024届高三第一次调研考试数学试卷
广东省深圳市2024届高三第一次调研考试数学试卷湖南省邵阳市邵东市第一中学2023-2024学年高二下学期3月月考数学试题广东省广州市白云中学2023-2024学年高三下学期零模(3月月考)数学试题(已下线)专题10 切线问题【讲】(已下线)压轴题03不等式压轴题13题型汇总-2(已下线)第01讲 导数的概念及其意义、导数的运算(十二大题型)(讲义)-2(已下线)重难点突破03 三次函数的图象和性质 (八大题型)-1
名校
5 . 如图,对于曲线G所在平面内的点O,若存在以O为顶点的角
,使得对于曲线G上的任意两个不同的点
恒有
成立,则称角
为曲线G的相对于点O的“界角”,并称其中最小的“界角”为曲线G的相对于点O的“确界角”.已知曲线C:
(其中e是自然对数的底数),点O为坐标原点,曲线C的相对于点O的“确界角”为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75afceb135e4ac785f39844702563f32.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7177a92a7fe1bde8050b258b8310513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae008f237c3360defae5da277a9d0f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75afceb135e4ac785f39844702563f32.png)
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2023-11-17更新
|
418次组卷
|
5卷引用:江苏省连云港市2023-2024学年高三上学期期中数学试题
江苏省连云港市2023-2024学年高三上学期期中数学试题河北省部分高中2024届高三上学期期末数学试题(已下线)黄金卷05(已下线)专题10 切线问题【讲】甘肃省白银市靖远县第一中学2024届高三下学期模拟预测数学试题
6 . 已知函数
有三个不同的零点,则实数
的范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81d4867510891f84fb4e3054f3c2f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
7 . 如果两地的距离是600公里,驾车走完这600公里耗时6小时,那么在某一时刻,车速必定会达到平均速度100公里/小时.上述问题转换成数学语言:
是距离关于时间的函数,那么一定存在:
就是
时刻的瞬时速度.前提条件是函数
在
上连续,
在
内可导,且
.也就是在曲线的两点间作一条割线,割线的斜率就是
是与割线平行的一条切线的斜率,切线与曲线相切于
点.已知对任意实数
,且
,不等式
恒成立,若函数
,则实数
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/287c9c5995ec50cc94287fced027889a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dcee29fdf5ec1ebd5f00c494c3fcb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a762c6499655b73518909f2d77fd505.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c7705841e16ef353eae8a3aea643c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2210f152080d9a68a97c805f5c1cde96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c898787dd05d6f1f1d67b7a9b97ede5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0180418ce0bba1def29ed37df967f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2023-08-04更新
|
282次组卷
|
3卷引用:山东省潍坊市临朐县第一中学2022-2023学年高三上学期9月月考数学试题
名校
8 . 设
,
,A、D为曲线
上两点,B,C为曲线
上两点,且四边形ABCD为矩形,则实数b的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4bd98950fa184af6ba0b4559b968e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81d4d11daf8b4f9fb3bdc7f648114714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
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9 . 已知抛物线
,点
在直线
上,过点
作
的2条切线,分别交
轴于点
、
,则
的最小值为______ ,
的外接圆面积的最小值为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c608def11fa0e2b34f05592ef1d11fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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2022高三·全国·专题练习
解题方法
10 . 已知双曲线
,点
在双曲线
上,点
在直线
上,
的倾斜角
,且
,双曲线
在点
处的切线与
平行,则
的面积的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168043af65ed01123fe7ed63ee7b3cd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3016baf1a9ce777f16ea9ce469b2510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0483c22ee3e2dce5b8c155dcd2b6ab3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ee4444e887a71849bfd73d352e1f4d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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