23-24高二上·上海·课后作业
解题方法
1 . 利用向量证明:如果一条直线垂直于一个平面内的两条相交直线,那么这条直线垂直于这个平面(即垂直于这个平面中的任何直线)
已知:如图,
、
是平面
内的两条相交直线,直线
满足
,
.求证:
.
已知:如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff290c28b42c8380283f6259daaec5c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac16b6d9ffc65507c5cd4083a1363937.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e380108ba2cf04e68a5a9393d2b921c.png)
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名校
解题方法
2 . 已知椭圆
过点
,且离心率为
.设
,
为椭圆
的左、右顶点,
为椭圆上异于
,
的一点,直线
,
分别与直线
相交于
,
两点,且直线
与椭圆
交于另一点
.
(1)求椭圆
的标准方程;
(2)求证:直线
与
的斜率之积为定值;
(3)判断三点
,
,
是否共线:并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310f780f4f03699023b1322a1e002539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/c5db41a1f31d6baee7c69990811edb9f.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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
(3)判断三点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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2022-10-11更新
|
1675次组卷
|
9卷引用:江苏省金陵中学集团南京市人民中学2021-2022学年高二上学期10月月考数学试题
20-21高二·江苏·课后作业
名校
3 . 从函数角度看,
可以看成以r为自变量的函数
,其定义域是
.
(1)画出函数
的图象;
(2)求证:
;
(3)试利用(2)的结论来证明:当n为偶数时,
的展开式最中间一项的二项式系数最大;当n为奇数时,
的展开式最中间两项的二项式系数相等且最大.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afb4fb20d3a3a67baa8505623e0bd9de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfaf2264554dc5fa6e7c20799ef9987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed3d1035e120d16bddf30c56bd475a9e.png)
(1)画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec77fa26a2c9e640dc5c9611fd5a6a5.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69ca11d3c6898eec906c4597ef0c4418.png)
(3)试利用(2)的结论来证明:当n为偶数时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5abcb3802cf02be93a8c89067bd49a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5abcb3802cf02be93a8c89067bd49a.png)
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2021-12-06更新
|
490次组卷
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4卷引用:7.4二项式定理
4 . 下列各题在应用数学归纳法证明的过程中,有没有错误?如果有错误,错在哪里?
(1)求证:当
时,
.
证明:假设当
时,等式成立,即
.
则当
时,左边
=右边.
所以当
时,等式也成立.
由此得出,对任何
,等式
都成立.
(2)用数学归纳法证明等差数列的前n项和公式是
.
证明,①当
时,左边=
,右边
,等式成立.
②假设当
时,等式成立,即
.则当
时,
,
.
上面两式相加并除以2,可得
,
即当
时,等式也成立.
由①②可知,等差数列的前n项和公式是
(1)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57a93680033e45aa7f4226edcdd0d0c.png)
证明:假设当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769becde4d8d0c1b487c727bd562bb1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0025cda4a1182a9341e28cf021b3d963.png)
则当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7f6974560f10fa3047f2f6bf77bc1ed.png)
所以当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
由此得出,对任何
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1933b7c3ace69622339353431c519b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57a93680033e45aa7f4226edcdd0d0c.png)
(2)用数学归纳法证明等差数列的前n项和公式是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba269108f5612e25822bce40eab39a59.png)
证明,①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87b351f16728b0023fd63678f8103c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5202cc8a5f8259b25ba31346feafcfe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4704eff3c92eaa4e6b040c4bbb542b.png)
②假设当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/769becde4d8d0c1b487c727bd562bb1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0915a8cffc2076e75fdda3484e3f5a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d19930a09d20a1b2497702a0d2211183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de1ca469cabd255b7fbe8179ae8f6630.png)
上面两式相加并除以2,可得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff62fdb872da6debad99b36880d61a6.png)
即当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ba21f3d0cfc86d40e2e06446623ce0.png)
由①②可知,等差数列的前n项和公式是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba269108f5612e25822bce40eab39a59.png)
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5卷引用:人教A版(2019) 选择性必修第二册 新高考名师导学 第四章 4.4 数学归纳法
5 . 分析法又称执果索因法.若用分析法证明“设
,且
,求证:
”索的因应是______ .
①
;②
;③
;④
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce613eaa5df46a50174085ef5d1087fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e56f4504e0f80fd031c8b5f41832e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bff6d61a8eaff20b364a9e3235577c69.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481ee0d1e39e92a4732eea90225eb94c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6e90787c63ca5b5f1a45e0f6e85aaa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8062c16e427bcf70b7ab5c94e8f25a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40e5c797b097deb1f9e89bcb3a405f1.png)
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6 . 设函数
,
为
的导函数,
,
.
(1)用a,b表示c,并证明:当
时,
;
(2)若
,
,
,求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e36fc3f9b69c79fa9f0f4835a8b611b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a15bccf9756ec716bd5c04e2641b6441.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dd91f855de4fead61c578e4f5170b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799f6009a476fa056e1af71f26dd2fd0.png)
(1)用a,b表示c,并证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c42f148508576752d87c43c2526eec5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9222ffc26c0e6bfbf252ab5d8a520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03837b3769eda7f0d3804cc5ad4a6d60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ebd8ae3481f1362c42b47af65a38d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2fb40a36a293471742ce75f6b9635b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c27ec39e50eba15ba551a58677bc73c9.png)
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7 .
已知正数
,
,
成等差数列,且公差
,求证:
,
,
不可能是等差数列.
设实数
,整数
,
.证明:当
且
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/812be9806122241c476ba1db516c4823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c70fcaa661df4fbcad820b439accda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9237dbe3a4f28962ef2870b4e7dab599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d26302e47e2926b0e807952b0efe7463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cec12441802f71e803efaf2c62ee588.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dab9e79198239cda875305fd6809b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b98ef143f8159f3a7dafa1fd2f2370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adc3e5be1796493161a4df7e28a6f6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01710dd52c8fcfd6253697797b330453.png)
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解题方法
8 . 已知函数
(
,
为自然对数的底数),
是
的导数.
(1)当
时,求证:
;
(2)是否存在整数
,使得
对一切
恒成立?若存在,求出
的最大值,并证明你的结论;若不存在,也请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbc62bb186214f638ae7eb5600a90b16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
(2)是否存在整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91b7c3887ad1e4cc1d71a6c04645806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-03-22更新
|
427次组卷
|
4卷引用:福建省福鼎第一中学2021-2022学年高二下学期第一次月考数学试题
福建省福鼎第一中学2021-2022学年高二下学期第一次月考数学试题2020届福建省福州第一中学高三下学期教学反馈检测数学(理)试题(已下线)2020届高三3月第01期(考点03)(理科)-《新题速递·数学》安徽省芜湖市第一中学2020届高三下学期3月第五次线上考试数学试题
名校
解题方法
9 . 如图,在三棱锥
中,
是边长为1的正三角形,
,
.
![](https://img.xkw.com/dksih/QBM/2020/2/13/2398365843947520/2399460610719745/STEM/40cce10b92dc4bab90d2a74bfc1724ac.png?resizew=234)
(1)求证:
;
(2)点
是棱
的中点,点P在底面
内的射影为点
,证明:
平面
;
(3)求直线
和平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c24b7a9466a1e35328a8a4b1ba7fa84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d60df9713216819939438d60fdc3e3f.png)
![](https://img.xkw.com/dksih/QBM/2020/2/13/2398365843947520/2399460610719745/STEM/40cce10b92dc4bab90d2a74bfc1724ac.png?resizew=234)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e35a6cf772fbe75c29b6c27193b3c9a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
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