名校
1 . 已知
的导数存在,
的图象如图所示,设
是由曲线
与直线
,
及x轴围成的平面图形的面积,则在区间
上( )
![](https://img.xkw.com/dksih/QBM/2022/5/13/2978332261089280/2978421994168320/STEM/b2e475dc-1642-4e61-ad96-bdf6cc9a981f.png?resizew=150)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50fad31f02e652b0225b4d7a6057421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://img.xkw.com/dksih/QBM/2022/5/13/2978332261089280/2978421994168320/STEM/b2e475dc-1642-4e61-ad96-bdf6cc9a981f.png?resizew=150)
A.![]() ![]() ![]() | B.![]() ![]() ![]() |
C.![]() ![]() ![]() | D.![]() ![]() ![]() |
您最近一年使用:0次
2022-05-13更新
|
560次组卷
|
5卷引用:2020年清华大学强基计划招生考试数学试题
解题方法
2 . 已知点P在双曲线
上,分别过P点作渐近线的平行线交x轴于点A,B且A点在靠近原点一侧,过A点作x轴的垂线交以
为直径的圆于点C,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a0bd4bd9985f1e367c100b453ed03f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
您最近一年使用:0次
3 . 已知实数x,y,z满足
则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7c36ff72b21dd9ea1cfcaa444f0164.png)
A.![]() | B.![]() |
C.x,y,z均为有理数 | D.x,y,z均为无理数 |
您最近一年使用:0次
解题方法
4 . 如图,开口向右的抛物线对称轴与x轴重合,焦点位于坐标原点处,并且过点
.设直线
与抛物线交于
两点,直线
看与抛物线交于
两点.
![](https://img.xkw.com/dksih/QBM/2023/2/7/3169711929909248/3169843440074752/STEM/cdb8ea8fb97149f8848f61456cc00bd0.png?resizew=317)
(1)求抛物线方程.
(2)求证:
.
(3)设直线
分别与y轴交于P,Q两点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc756fb11c7c96bf318b5fae4982f507.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47aca422a33ec9b9430d204659ff9fbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c345dfe2ac9387357be143c0b96de6ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/756f66428eba953d4610f59a3479d143.png)
![](https://img.xkw.com/dksih/QBM/2023/2/7/3169711929909248/3169843440074752/STEM/cdb8ea8fb97149f8848f61456cc00bd0.png?resizew=317)
(1)求抛物线方程.
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d298273d6dc5a07cc6f819ac3e63730.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15abfafc59b6f9f01f3be4db4df797d.png)
您最近一年使用:0次
5 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46aa11e277aa28dda397af5ba51aa708.png)
A.不等式![]() ![]() |
B.不等式![]() ![]() |
C.直线![]() ![]() |
D.直线![]() ![]() |
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6 .
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11fc1bd08f8ea027c1d2846ed8f4f0ab.png)
A.1 | B.2 | C.![]() | D.![]() |
您最近一年使用:0次
7 . 已知罗尔中值定理:若函数
满足:①
在
上连续;②
在
上可异;③
,则存在
,使得
.
(1)试证明拉格朗日中值定理:若函数
满足:①
在
们上连续;②
在
上可导,则存在
,使得
.
(2)设
的定义域与值域均为
且
在其定义域上连续且可导.求证:对任意正整数n,存在互不相同的
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f94345694d4215284c41f87146795ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8166cc061d434d02bccbcf153cc6b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be227e1da97582fd99cb7cec416982af.png)
(1)试证明拉格朗日中值定理:若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4776c85b79df196f606d3ebf3697fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8166cc061d434d02bccbcf153cc6b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7853db400c62dc688f01aa38be72acd2.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a61eaad9616cce2705245cc7ffc2636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05eca773cea4fc8732050ab44063aa3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5932903a7ddb5fe53eff8249c6cd3619.png)
您最近一年使用:0次
解题方法
8 . 已知双曲线
,直线l与双曲线C的右支交于A,B两点,记
,其中O为坐标原点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4174368661841cb1c9acbce1ddfb57e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0c8f7a21d9693033b49c83a66706192.png)
A.m的最小值为2,且此时l与x轴平行 | B.m的最小值为2,且此时l与x轴垂直 |
C.m的最大值为2,且此时l与x轴平行 | D.m的最大值为2,且此时l与x轴垂直 |
您最近一年使用:0次
2021-09-07更新
|
263次组卷
|
4卷引用:2017年清华大学THUSSAT附加科目测试数学试题(二测)
2017年清华大学THUSSAT附加科目测试数学试题(二测)湖南省2021届高三下学期高考冲刺试卷(一)数学试题(已下线)考向43 直线与圆锥曲线(已下线)专题13 圆锥曲线-备战2022年高考数学(文)母题题源解密(全国乙卷)
9 . 设正整数
使得关于
的方程
在区间
内恰有
个实根
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64170fd8ac03379ffe24249e730000d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40622f9501f8a4e6eb8a3bb13bb655f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4acd5e05f89802149b8b810c24d6ac73.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() ![]() ![]() |
您最近一年使用:0次