1 . 已知函数
.
(1)若
在
上单调递增,求实数a的取值范围;
(2)当
时.
(i)求证:函数
在
上单调递增;
(ii)设区间
(其中
),证明:存在实数
,使得函数
在区间I上总存在极值点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef290c72466c30bc20d7414418cfaee.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(i)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1899b95e2442b6a08a5a134b36ed7c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
(ii)设区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e07062bde69560336def001c925eb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb9dfa7ecdfa37e643c51193a388836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d8047f0a8bd0cf4e250cd0fe80093b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbd86a6b6493a67696125835eea5f76.png)
您最近一年使用:0次
名校
2 . 已知函数
,其中
.
(Ⅰ)讨论
的单调性;
(Ⅱ)当
时,证明:
;
(Ⅲ)求证:对任意正整数n,都有
(其中e≈2.7183为自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa9f7cb75c5500ad56dfe0f178dedb92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
(Ⅰ)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257810d08006d4b886331966c99767ea.png)
(Ⅲ)求证:对任意正整数n,都有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf0f4b1e329db4bf6070f993297f9b9.png)
您最近一年使用:0次
2019-01-12更新
|
4102次组卷
|
10卷引用:江西省五市八校2019-2020学年高三第二次联考文科数学试题
江西省五市八校2019-2020学年高三第二次联考文科数学试题【区级联考】天津市蓟州等部分区2019届高三上学期期末联考数学(文)试题【区级联考】天津市部分区2019届高三(上)期末数学(文科)试题【全国百强校】四川省成都市成都外国语学校2018-2019学年高二下学期期中考试文科数学试题【全国百强校】河北省武邑中学2019届高三下学期第一次模拟考试数学(文)试题湖北省武汉二中2019-2020学年高二下学期4月第二次线上测试数学试题四川省宜宾市第四中学校2019-2020学年高二下学期期中考试数学(理)试题四川省宜宾市第四中学校2019-2020学年高二下学期期中考试数学(文)试题广东省佛山市三水区三水中学2019-2020学年高二下学期第二次统考数学试题黑龙江省大庆实验中学2019届高三普通高等学校招生全国统一考试文科数学模拟试题
名校
解题方法
3 . 已知椭圆
过点
,离心率为
.
(1)求椭圆的标准方程;
(2)过椭圆的上顶点作直线
交抛物线
于
、
两点,
为原点.
①求证:
;
②设
、
分别与椭圆相交于
、
两点,过原点
作直线
的垂线
,垂足为
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c9bebea391a1f9956dfcca98d9d1f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c778b2d3185e80c9c00cd6fe156d95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆的标准方程;
(2)过椭圆的上顶点作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f4123c19136d3a4dc040dce8e34e14.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/1dde8112e8eb968fd042418dd632759e.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4cd68cc82e90a5e2049a7ea3171b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a31666076b1d37cd2f99afa950da5ab.png)
您最近一年使用:0次
2017-11-29更新
|
1317次组卷
|
4卷引用:江西省南昌市第二中学2017-2018学年高二上学期期中考数学(文)试题
4 . 设
,
,函数
在
与
处取得极值.
(1)求实数a,b的值;
(2)若
,求证:当
时,
恒成立;
(3)证明:若
,则
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b6561cab7979352279613ef4f1c51d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f09e7922457f13b44b4e7402520abab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
(1)求实数a,b的值;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540864f4f09756707102e5e2c363d91e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc1af8d9b2b197c76495602e894916e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d072c7c23746459f447b26363db6af.png)
(3)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7ba98a91f8d890daedca91e3cc778c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9ab6e1543588872063a6b4794f4e961.png)
您最近一年使用:0次
名校
5 . 已知函数
,
.
(1)若
,讨论函数
的单调性;
(2)若
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd58e16598e6bdb3c35194af69951a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895938bc4691b6ad48f8b001dfcad102.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074408cfb3eedc559116996d57d5a087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4175c57c61b71897b10583ad32e5e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47c95440ace01be940f1591eed18ab5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f78ae07b1452e4f9dd8ba93db61d17.png)
您最近一年使用:0次
2024-06-05更新
|
271次组卷
|
2卷引用:江西省临川第二中学2023-2024学年高二下学期6月月考数学试题
解题方法
6 . 已知椭圆
的离心率为
,且a,b的等比中项为2.
(1)求C的方程;
(2)若直线
与C交于点A,B两点,直线
过点A且与C交于另外一点
,直线
过点B,且与C交于另外一点
.
(ⅰ)设
,
,证明:
;
(ⅱ)若直线
的斜率为
,判断是否存在常数m,使得k是m,
的等比中项,若存在,求出m的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b343d77ee4dced82ecc479206c42977d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e82f042b992b3c56a7a0ba26033aef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93f427c66fb1e0c7bc55dc741867d9fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
(ⅰ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c848021933bfdfc20370d7a188aa356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcbe0f3e0c41f79c15cbae31aa979065.png)
(ⅱ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7e08d5c04f0431fb57b33a01717b599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110ee60613ccf45d772870bc9297c708.png)
您最近一年使用:0次
7 . 已知
且
.
(1)当
时,求证:
在
上单调递增;
(2)设
,已知
,有不等式
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b9e1ee18c04dbe1c9beaf49fa67207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0ffecb03c47be920254c4ccffa5b222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6408a113793f7d7aa6b430d436d711d0.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db8f867196410e2828e2bbd3183b02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7c48c1bbf3082d238c355fb0f616622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
解题方法
8 . 已知
是双曲线
:
上的一个点,且与两焦点构成的三角形的面积是
.
(1)求双曲线
的标准方程;
(2)
是
的右顶点,过点
的直线
与
交于异于
的不同两点
、
,与直线
交于
点.连接
,并过
作
的平行线分别与直线
、
交于
、
两点.求证:
是线段
的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfbaf6522c9a1fb737b9712dbcb34247.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177ae60ade0b7ac20e7bdc40eaa1ef5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2348e3eb68118c6f7c6132c546525ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b94469fd19f40116e2dec334919d6586.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
9 . 已知函数
,
.
(1)当
时,求函数
的极值;
(2)已知实数
.
①求证:函数
有且仅有一个零点;
②设该零点为
,若
图象上有且只有一对点
,
关于点
成中心对称,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fe84ecdcafb66c2e3a4dd702503729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068eeacfc105bcd3cb3e547a9cc3f39c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38ada7012b4fd07e9d345c87f346157.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)已知实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed0c40f94da9ef7dc21e296235b2326a.png)
①求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
②设该零点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad9a4881ebe1a4a566d0fab96d71baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9938230f82e91cf09f8157b532baaba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
10 . 如图所示,用一个不平行于圆柱底面的平面,截该圆柱所得的截面为椭圆面,得到的几何体称之为“斜截圆柱”.图一与图二是完全相同的“斜截圆柱”,AB是底面圆
的直径,
,椭圆所在平面垂直于平面ABCD,且与底面所成二面角为
,图一中,点
是椭圆上的动点,点
在底面上的投影为点
,图二中,椭圆上的点
在底面上的投影分别为
,且
均在直径AB的同一侧.
时,求
的长度;
(2)(i)当
时,若图二中,点
将半圆均分成7等份,求
;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526908dfb46cf151b8ab1492a9d52047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1d663b6001346d11600f064cfcb7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d26ebb800066a7bce57213cd074005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d26ebb800066a7bce57213cd074005.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b20bf4f818b494e7b5fa9c68527026e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893ff0f9b64c66312c37cb7ce90c351d.png)
(2)(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c345907ebe27888332b1b44c666cc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bde134aa77da12366e6a742fa33b4bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e578d74f75cf5a087cb5dbad1d07c66.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0838e80d58bad3e9cbc4766d2a0ec3.png)
您最近一年使用:0次