名校
解题方法
1 . 《见微知著》谈到:从一个简单的经典问题出发,从特殊到一般,由简单到复杂,从部分到整体,由低维到高维,知识与方法上的类比是探索发展的重要途径,是发现新问题、新结论的重要方法.
例如,已知
,求证:
.
证明:原式
.
波利亚在《怎样解题》中也指出:“当你找到第一个蘑菇或作出第一个发现后,再四处看看,他们总是成群生长.”类似上述问题,我们有更多的式子满足以上特征.
请根据上述材料解答下列问题:
(1)已知
,求
的值;
(2)若
,解方程
;
(3)若正数
满足
,求
的最小值.
例如,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180409002586c7e3c2e06f6fdd742f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45fc0d73e11222c72a9afbfa9d091b3.png)
证明:原式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4b25c598517637dc8234d567f344be.png)
波利亚在《怎样解题》中也指出:“当你找到第一个蘑菇或作出第一个发现后,再四处看看,他们总是成群生长.”类似上述问题,我们有更多的式子满足以上特征.
请根据上述材料解答下列问题:
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180409002586c7e3c2e06f6fdd742f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e62883c4d3d8de9ac5b8eed793d5bd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52431587ef305ddb410bece4a6d76ee3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d91c584d15767339f6e84b78dddaf9b.png)
(3)若正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c48e4da908f869244dd5ba4dd3b4a79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180409002586c7e3c2e06f6fdd742f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46efe66dfaaf30d5f5969a4d1d6b8414.png)
您最近一年使用:0次
2022-10-21更新
|
437次组卷
|
4卷引用:四川省攀枝花市第三高级中学校2023-2024学年高一上学期10月月考数学试题
四川省攀枝花市第三高级中学校2023-2024学年高一上学期10月月考数学试题广东省中山市2022-2023学年高一上学期第一次调研数学试题四川省成都市第七中学2023年高三上学期1月月考数学文科试题(已下线)第03讲 第二章 一元二次函数、方程和不等式章节综合测试-【练透核心考点】
名校
2 . 如图,在边长为
的正方形
中,点
是
的中点,点
是
的中点,点
是
上的点,且
.将△AED,△DCF分别沿
,
折起,使
,
两点重合于
,连接
,
.
![](https://img.xkw.com/dksih/QBM/2018/7/16/1989574276603904/1989768106516480/STEM/88df25c0416e4c0fbd0694a6e48537a8.png?resizew=318)
(Ⅰ)求证:
;
(Ⅱ)试判断
与平面
的位置关系,并给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1df842ffd4121b27c70a8d0b1f78b173.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2018/7/16/1989574276603904/1989768106516480/STEM/88df25c0416e4c0fbd0694a6e48537a8.png?resizew=318)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6969b9971ceae406072933356189a897.png)
(Ⅱ)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc704b98f4ed2c7359a7a5b6498b5290.png)
您最近一年使用:0次
2018-07-16更新
|
689次组卷
|
3卷引用:【全国市级联考】四川省攀枝花市2017-2018学年高二下学期期末调研检测数学(理)试题
名校
3 . 如图所示,在梯形
中,
,
,
.四边形
为矩形,且
平面
.
平面
;
(2)若直线
与
所成角的正切值为
,点
在线段
上运动,当点
在什么位置时,平面
与平面
所成的锐二面角的余弦值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f18f1b5ebe17b068fe79bdf30d6effc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b0382c28547d3834ca71f3f0677695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc56d42b003cbcb1fbe5c50e55b26b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b72906641ed13716cfbce50923282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619096595112f0340a43b756e114dd3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2db1674add0f4a1a24f5ed893b1c5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e108d5c61e85e0741ec2c484fc5768.png)
您最近一年使用:0次
2024-01-31更新
|
1203次组卷
|
5卷引用:四川省攀枝花市普通高中2023-2024学年高二上学期教学质量监测数学试题卷
四川省攀枝花市普通高中2023-2024学年高二上学期教学质量监测数学试题卷2024届高三新改革适应性模拟测试数学试卷二(九省联考题型)(已下线)第5讲:立体几何中的动态问题【练】(已下线)黄金卷04(2024新题型)新疆生产建设兵团第三师图木舒克市第一中学2023-2024学年高二下学期数学开学考试数学试卷
4 . 如图,直三棱柱
中,
,点
在线段
上,且
,
.
为
的重心;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9073cce40aa78cc9693c988f3eea90aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47af45fbf1714055d9b414a44a8613fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166ccfa0ac0388903f3f5960c7fa3660.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e223e3d40ee025f15ead90746c28b8c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167e4b949f6bda469c5ac4af5a85a0db.png)
您最近一年使用:0次
解题方法
5 . 如图,直三棱柱
中,
,点
在线段
上,且点
为
的重心,
.
(1)证明:
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/166ccfa0ac0388903f3f5960c7fa3660.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9073cce40aa78cc9693c988f3eea90aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/28/cee33231-7318-4af2-9650-8412edb4e57e.png?resizew=140)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47af45fbf1714055d9b414a44a8613fa.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e223e3d40ee025f15ead90746c28b8c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e7135d2f756584a391268253dcea52.png)
您最近一年使用:0次
6 . 如图,四棱锥
中,
底面
,
,
,
,
为线段
上一点,且
,
为
的中点.
(1)证明:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40fa25439480bdff3d4ba45634f514c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db8679b329b17bc65022bd1a1418632b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/e908eb93-d482-4a65-b940-072b7c782cd9.png?resizew=171)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1885efcff0b903e314057dd153578600.png)
您最近一年使用:0次
名校
解题方法
7 . 已知椭圆
的右焦点是F,上顶点A是抛物线
的焦点,直线
的斜率为
.
(1)求椭圆C的标准方程;
(2)直线
与椭圆C交于P、Q两点,
的中点为M,当
时,证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
(1)求椭圆C的标准方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6068a99026c27433a7fc8932a5d282a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7be008afbf741d994ca8c851e98007.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2024-01-17更新
|
1062次组卷
|
4卷引用:四川省攀枝花市2024届高三二模数学(理)试题
四川省攀枝花市2024届高三二模数学(理)试题(已下线)专题06 直线与圆、椭圆方程(分层练)(三大题型+12道精选真题)黑龙江省哈尔滨市第一二二中学校2023-2024学年高二下学期3月月考数学试题宁夏吴忠市2024届高三下学期高考模拟联考试卷(二)理科数学试题
8 . 如图,在几何体
中,四边形
是等腰梯形,四边形
是矩形,且平面
平面
,
,
分别是
的中点.
;
(2)若点
到平面
的距离是
,求
与平面
所成的线面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5a68a008a22d5a8cea5fe8dcf31e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba74e936c53298ad7a545afc2d1b83d.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/4e88ee337b7c9082f4fe84fd1752d55a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84be64d28b1623e71ad989f37336b1f2.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70db40c42655327adee01caedfc9d50c.png)
您最近一年使用:0次
9 . 如图,在直四棱柱
中,底面
是直角梯形,
∥
,且
.
平面
;
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55ea1e0580694b3c596ede8b76ef6857.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2512ffe4864827d4aeaa1394ba01eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
您最近一年使用:0次
10 . 已知数列
的前
项和为
.数列
的首项
,且满足
.
(1)求数列
的通项公式;
(2)求证:数列
为等比数列;
(3)设
,求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce817f902302ebdd5a599e43df77614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a24e6bcf49b8e45531a2d4e4c70c181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4f5adeb7f0306906a47224fbf95328.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd8dabdd9fa8bbbfe7f96bc6dd7cd7a.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c2a5f8ec179b72b201c3c0a670612a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
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2024-01-31更新
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3卷引用:四川省攀枝花市普通高中2023-2024学年高二上学期教学质量监测数学试题卷