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解题方法
1 . 现有
个编号为
的小球,随机将它们分成甲、乙两组,每组
个. 设甲组中小球的最小编号为
,最大编号为
;乙组中小球的最小编号为
,最大编号为
记
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af08d7880119cf28597caa5b8bc2318b.png)
(1)当
时,求
的分布列和数学期望;
(2)令
表示“事件
与
的取值恰好相等”.
①求事件
发生的概率
;
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d51f9147b8265c0276c1f2c2659197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cd1cd466cd9c2efac66912e0d4cd188.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbda50272b74d847ec25ee9bf89b48ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f38b2f8c48333ec2e7749a83fcd0c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af08d7880119cf28597caa5b8bc2318b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b734e8f1546481e3eb4976008a045de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1116ce7f5a1a7b57517276d5092fa.png)
①求事件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a244cf6ac956323ea14e09c5e175448.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cd2de30ea549eddd97b1a1c81bf092.png)
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2 . 约数,又称因数.它的定义如下:若整数a除以整数m(
)除得的商正好是整数而没有余数,我们就称a为m的倍数,称m为a的约数.
设正整数a有k个正约数,即为
,
,⋯
,
,(
).
(1)当
时,是否存在
,
,…,
构成等比数列,若存在请写出一个满足条件的正整数a的值,若不存在请说明理由;
(2)当
时,若
,
,⋯
构成等比数列,求正整数a.
(3)当
时,若
,
,…,
是a的所有正约数的一个排列,那么
,
,
,⋯,
是否是另一个正整数的所有正约数的一个排列?并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
设正整数a有k个正约数,即为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c0cd13ec90e5697013e59d73d3e82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df21efb81bd9f5ec47c8ad705a2272ad.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835c74bbb8c61dd2d2f008664a8c8810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeaed9ec21e090defafcfeefe0059c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe164d8a8a4049e01565b576007651de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01416ee1d48b17f889e444b7eda99740.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/177e4374fb738c4f13dc58e9025c88e4.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835c74bbb8c61dd2d2f008664a8c8810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6f19b84484b5480ea2100165abfd81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f9d2e152db0845ff23e4ea0cd00974d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f30fd21924e7bcf368854ef38af82e.png)
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3 . 类比于平面三角形中的余弦定理,我们得到三维空间中的三面角余弦定理:如图1,由射线
、
、
构成的三面角
,
,
,
,二面角
的大小为
,则
.
中,平面
平面
,
,
,求
的余弦值;
(2)当
时,证明以上三面角余弦定理;
(3)如图3,斜三棱柱
中侧面
,
,
的面积分别为
,
,
,记二面角
,二面角
,二面角
的大小分别为
,
,
,试猜想正弦定理在三维空间中推广的结论,并证明.
![](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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa26fadeee2becc192fa53d778445d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac229a5e782559ffb0f271cbfc01c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6ab2d197160f40b72fe0abb3fe527d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a438393ddfc7da1804baf4932442bb35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6a7725d31fb74e974e2e45ba56805a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70d708336d4f15e7fca0b26acb353b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73152c2b4298298c8b81dc16dc21f5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947c03e48c4be7485f1547817f890c53.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291e4e0dc7974f2ce1b59620e3ec0232.png)
(3)如图3,斜三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa84da7ead562cffd02afd5940f8aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1654dfe63f11563eadbaee32dae7b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0cebc1b9472488bfb8f0db1c723fef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8d4017e1a37acb0c8e00508be472b2.png)
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4 . 已知函数
,其中
.
(1)当
时,
,求a的取值范围.
(2)若
,证明:
有三个零点
,
,
(
),且
,
,
成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d8543507212b830a2a03d4a8f6d139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c164755dc2d7cff80fb4c9cffc9be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301605e86e5a5e61a65c91cd3dd8b77e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
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5 . 在平面直角坐标系xOy中,A,B点的坐标分别为
和
,设
的面积为S,内切圆半径为r,当
时,记顶点M的轨迹为曲线C.
(1)求C的方程;
(2)已知点E,F,P,Q在C上,且直线EF与PQ相交于点A,记EF,PQ的斜率分别为
,
.
(i)设EF的中点为G,PQ的中点为H,证明:存在唯一常数
,使得当
时,
;
(ii)若
,当
最大时,求四边形EPFQ的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d06d31c9a2298b02664a86ddd91b1121.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cee9e51b1dd360d8e141e7fa8f4224d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b722e2e83c2d125453ee2d80a5e64d26.png)
(1)求C的方程;
(2)已知点E,F,P,Q在C上,且直线EF与PQ相交于点A,记EF,PQ的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
(i)设EF的中点为G,PQ的中点为H,证明:存在唯一常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f132407bf1cc9d1f460d50f1b0547993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43b3fa41635da8da11d6c04287ff7513.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129fa211eb0cfb3968d38c3c90249842.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7560c67fac3a45cf25ec33aa3ca52519.png)
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6 . 已知抛物线
为第一象限内
上任意一点,以
为切点作
的切线
与
轴交于点
,与
轴交于点
,过点
作垂直于
的直线
交
于
两点,其中点
在第一象限,设
与
轴交于点
.
(1)若点
的坐标为
,求切线
的方程;
(2)若
,求
的值;
(3)当
时,连接
,记
的面积分别为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4498a6eea5157b692de2c3ff77320d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441f75e926cf159eee619685312bb4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e81a1e6338c6da07a6e8dfaafdffb34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7a95ad057dc0d06ab143b1282fbb56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9c48b75c90321b2051f20ac5e788ae.png)
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7 . 若数列
的各项均为正数,且对任意的相邻三项
,都满足
,则称该数列为“对数性凸数列”,若对任意的相邻三项
,都满足
则称该数列为“凸数列”.
(1)已知正项数列
是一个“凸数列”,且
,(其中
为自然常数,
),证明:数列
是一个“对数性凸数列”,且有
;
(2)若关于
的函数
有三个零点,其中
.证明:数列
是一个“对数性凸数列”:
(3)设正项数列
是一个“对数性凸数列”,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5323231f6376db726f6fba9dd53b97a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/345367d7aac000974ce1e3cf4ce1b15a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5323231f6376db726f6fba9dd53b97a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870910beaaf7bd60242701ad7ddaf06b.png)
(1)已知正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6a11176eb502db16e19c38278b77e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/930bc56406e69b785b37a83d48e36724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1e49907ec00414cee66b1d082183fb.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fe507c4d73de71c69ede4cfbdc7fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02ab7609f5b06fc564e8e588f378870.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a447e5baee4f7518706498d4aca7553b.png)
(3)设正项数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5330adb65f6c8bd64d0cad579ad2910c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ca2b0946db9bbcbce5f19507f5c485e.png)
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8 . 函数
是我们最熟悉的函数之一,它是奇函数,且y轴和直线
是它的渐近线,在第一象限和第三象限存在图象,其图象实质是圆锥曲线中的双曲线.
的图象不仅是中心对称图形,而且还是轴对称图形,求其对称轴l的方程;
(2)若保持原点不动,长度单位不变,只改变坐标轴的方向的坐标系的变换,叫坐标系的旋转,简称转轴.
(i)请采用适当的变换方法,求函数
变换后所对应的双曲线标准方程;
(ii)已知函数
图象上任一点到平面内定点
的距离差的绝对值为定值,以线段
为直径的圆与
的图象一个交点为
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
(2)若保持原点不动,长度单位不变,只改变坐标轴的方向的坐标系的变换,叫坐标系的旋转,简称转轴.
(i)请采用适当的变换方法,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
(ii)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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2024-06-15更新
|
75次组卷
|
2卷引用:山西省晋城市第一中学校2023-2024学年高二下学期第四次调研考试(5月)数学试题
名校
9 . 帕德近似是利用分式有理函数逼近任意函数的一种方法,定义分式函数
为
的
阶帕德逼近,其分子是m次多项式,分母是n次多项式,且满足
,
,
,…,
时,
为
在
处的帕德逼近.
(1)求函数
在
处的
阶帕德逼近
;
(2)已知函数
.
①讨论
的单调性;
②若
有3个不同零点
,
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbfee67d1c1cb26b67ef0fe3169e6dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd909ba3e40f03e2f58a4eed2e05f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcb8c6a69df1a0deaba265e204d5f99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047a8c1ed551fccee1c1848746c5f282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72029562177dfc99a171c9013eb90227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4573475f70860a3d99b92a329d0d07f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966dfe9109671c587892bd32f0b6699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b1868d9850b7103e1326eb001dfbce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb45f673c56a289ea78831c9237e8d20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58de4362237a2a719cde7c9049903da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9966dfe9109671c587892bd32f0b6699.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2adc63ce466d20e93f7d09d8b0bf9076.png)
①讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79fc0ce080b8ad8b63ba63259c680b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76e03829b4bbd1148c7f479ca409d436.png)
您最近一年使用:0次
名校
解题方法
10 . 已知椭圆C:
,过右焦点F的直线l交C于A,B两点,过点F与l垂直的直线交C于D,E两点,其中B,D在x轴上方,M,N分别为AB,DE的中点.当
轴时,
,椭圆C的离心率为
.
(2)证明:直线MN过定点,并求定点坐标;
(3)设G为直线AE与直线BD的交点,求△GMN面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165a501b2e6a3acc46212e59a166c053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff1c07d3ab5f594be5fffe13ebaaccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(2)证明:直线MN过定点,并求定点坐标;
(3)设G为直线AE与直线BD的交点,求△GMN面积的最小值.
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