1 . 帕德近似(Pade approximation)是法国数学家帕德(Pade)于l9世纪末提出的,其基本思想是将一个给定的函数表示成两个多项式之比的形式,具体是:给定两个正整数m,n,函数
在
处的
帕德近似为
,其中
,
,
,…,
(
为
的导数).已知函数
在
处的
阶帕德近似为
.
(1)求实数a,b的值;
(2)证明:当
时,
;并比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db527571cfd256c515424c6f9d114284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b73a1e9e6afa355710753d576ea991a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8cd76f42911e8c8e57ce761b4541137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c52140f46c02b2bde412f89d0977bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c85cd03aea30c3ee0093afad048b75c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b63504a4bf0d4861de7909bbc2e4878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd370c3b127fbdb77b6e5c40318328d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2db1e56c92e2ebdc5d2cae336a01b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e96546b3259afe4add331673fb835c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d307aa65d930bc8e51835eb147de513.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96d128f7851b7771f95bffbdbf3ced02.png)
(1)求实数a,b的值;
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d0af421900f7a55f52dd805064f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4548db97a06a6f27db6af1dd9b063645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/786a32019158f0d2ec126cf189ccf572.png)
您最近一年使用:0次
解题方法
2 . 已知A,B分别是椭圆
的左、右顶点,R为椭圆C上异于A,B的一点,且满足
.
(1)求椭圆C的标准方程;
(2)已知点
,过点
的直线交椭圆C于D,E两点,直线
,
分别交直线
于
两点,探究
是否为定值,若为定值,求出该定值;若不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19d5b538dbc0d6d7aca647794be954b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27117e63de9412bd33ac53f6a1971d3d.png)
(1)求椭圆C的标准方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0bea681006f614f8a070e9c6a942c04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c699a757a7ee06c063150def9c5dffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef9d0784478511736255074b9395fae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f30cb81835298cb612a828f355060a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/748e0ea9f0f974ea69fef4d04a0933d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e74181b941bc0f0cae3cc6a91309ce3.png)
您最近一年使用:0次
名校
解题方法
3 . 已知双曲线
的离心率为
,虚轴长为
.
(1)求双曲线C的方程;
(2)若动直线l与双曲线C恰有1个公共点,且分别与双曲线C的两条渐近线交于P,Q两点,O为坐标原点,证明:
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc2e6884bdcb0c1ae466765e291cc29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047616f1d1d39bf6c3cd07cf63ef5b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求双曲线C的方程;
(2)若动直线l与双曲线C恰有1个公共点,且分别与双曲线C的两条渐近线交于P,Q两点,O为坐标原点,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
您最近一年使用:0次
2024-06-14更新
|
469次组卷
|
4卷引用:贵州省遵义市2023-2024学年高二下学期5月期中联考数学试题
贵州省遵义市2023-2024学年高二下学期5月期中联考数学试题(已下线)宁夏回族自治区银川一中2024届高三下学期第四次模拟考试数学(理)试卷(已下线)宁夏回族自治区银川一中2024届高三下学期第四次模拟数学(文)试卷宁夏回族自治区银川一中2024届高三下学期第四次模拟考试数学(文)试卷
名校
解题方法
4 . 已知圆:
的圆心为椭圆
的右焦点
,且椭圆
的离心率为
.
(1)求椭圆
的标准方程;
(2)过点
且不与
轴重合的直线
交椭圆
于
两点,
为
的中点,
为坐标原点,分别过
作椭圆
的切线,两切线相交于点
.
(i)求证:
三点共线;
(ii)当
不与
轴垂直时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca2415dee662897b676734cfc768d66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(i)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3421e6965c86b4cca2a503385b3cc156.png)
(ii)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd5a5c9bf064e96f6c77cdd2b2951d8.png)
您最近一年使用:0次
名校
5 . 设
是函数
的导函数,若
可导,则称函数
的导函数为
的二阶导函数,记为
.若
有变号零点
,则称点
为曲线
的“拐点”.
(1)研究发现,任意三次函数
,曲线
都有“拐点”,且该“拐点”也是函数
的图象的对称中心.已知函数
的图象的对称中心为
,求函数
的解析式,并讨论
的单调性;
(2)已知函数
.
(i)求曲线
的“拐点”;
(ii)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10acd6d864583617dd3e71240bf0c857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43db00e106c7d08a76a7ba71ca5e63d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(1)研究发现,任意三次函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/012429b7101ba0f84e7b45598ed12db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211aed3f74a18399b2adbcb74420037e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e88ebfb5c0d6cce558b515be06404d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ea257a36c48ae67291bb79295085a5d.png)
(i)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2342ead0be84f52b93d85f167fdbb9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1bb642f5f896ed02ecd76d9a15e500.png)
您最近一年使用:0次
解题方法
6 . 在平面直角坐标系
中,已知直线
与抛物线C:
相切.
(1)求m的值;
(2)已知点
,
在抛物线C上,A,B分别位于第一象限和第四象限,且
,过A,B分别作直线
的垂线,垂足分别为
,
,当四边形
面积取最小值时,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec68c680d1b8c8cfa98b48a27d2c46a1.png)
(1)求m的值;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f8ec3a4456209b619d083b73f1218d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
7 . 已知实数x,y满足
,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f6ab027404b25dd4b24e2f28b898029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75e4db9cbb6496cce8141bddb83c51d6.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
8 . 已知函数
图象上的点
与方程
的解
一一对应,则下列选项中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0ec8aa466248a663cc603fdc06eeef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
A.![]() | B.0是![]() |
C.![]() ![]() | D.![]() |
您最近一年使用:0次
9 . 已知函数
在
上仅有两个零点,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd69e1358c1008079a5c9324f685e604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
解题方法
10 . 已知函数
.
(1)若
在定义域内不单调,求a的取值范围;
(2)证明:若
,且
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14dee98f762932a2b717636a20306b2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e4fb399cd59f3c65462df72b179a628.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f967a3906eff362ae1748b5a49f204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ed1fdfd6d053610f476731689209d32.png)
您最近一年使用:0次