名校
解题方法
1 . 如图,在三棱柱
中,侧面
是菱形,G是边
的中点.平面
平面
,
.
![](https://img.xkw.com/dksih/QBM/2020/10/20/2575283505111040/2578114044436480/STEM/bda0f61dc51048a48acc9ddc2cca33e9.png?resizew=215)
(1)求证:
;
(2)在线段
上是否存在点M,使得
平面
,若存在,请说明M点的具体位置,并证明你的结论;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c2e00a3b5d4f1e10a52058f148060d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9367449a5847eade07e69f4feddcb027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb64353c99068a7a1a8508a22f5b25b4.png)
![](https://img.xkw.com/dksih/QBM/2020/10/20/2575283505111040/2578114044436480/STEM/bda0f61dc51048a48acc9ddc2cca33e9.png?resizew=215)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a590a08b3823e01024de68e967cbf3f.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,在四棱锥
中,
,
,
,平面
平面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/d8dee249-e133-4f35-aca8-f9cbba1cddcc.png?resizew=180)
(1)求证:
;
(2)已知二面角
的余弦值为
.线段PC上是否存在点M,使得BM与平面PAC所成的角为30°?证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946470cef32a0bd769b3809351d8ee61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279e119eed905cf15026649a1b86502a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e4d19bf237a6fca67e0d01a9ddb726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/d8dee249-e133-4f35-aca8-f9cbba1cddcc.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545e18836bc7fee22f8f813a6f525d93.png)
(2)已知二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9f1e2b86f4eca37c72011d3dffb0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f1145c162038df3c7184d9201c628e.png)
您最近一年使用:0次
2021-01-13更新
|
974次组卷
|
5卷引用:福建省三明市2021届高三上学期期末质量检测数学试题
3 . (1)设
,证明:
.
(2)已知
,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ada798eeba5bd19d497bfd0741afd00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a737185eb85ca24cf66409ce1e09bc.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061813f1ec633c5c4c393c4de7938322.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fdd7a2eed12661bc4fe62fa8384355c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39ea7b40fb78703a118ab61820f6742f.png)
您最近一年使用:0次
4 . 已知四棱锥
中,
平面
,
,
,
,
是线段
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/9c683858-27b6-475d-9c08-1ae61f89853d.png?resizew=169)
(1)求证:
平面
;
(2)试在线段
上确定一点
,使得
平面
,并加以证明.
![](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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f779e7f5f53e4377b9a0a8e945d562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/051f092cbf89536d7e8b9fbf9d49355d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/9c683858-27b6-475d-9c08-1ae61f89853d.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34cf61780928291d51c7bbb08a5fcf81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)试在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d987bcf7114c002843702100444da017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
5 . 已知数列
满足
=1,
.
(Ⅰ)证明数列
是等比数列,并求
的通项公式;
(Ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3998df04d0a8ded946c3f39d545fdc7e.png)
(Ⅰ)证明数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(Ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffd3aa891969734bd23e0706fd56dda.png)
您最近一年使用:0次
名校
6 . 用反证法证明命题①:“已知
,求证:
”时,可假设“
”;命题②:“若
,则
或
”时,可假设“
或
”.以下结论正确的是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937559aeec06323cde8861b17024fc47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be100015cff38b6dfba5080fa94d128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe44dcfbe7130c760acae3703469dd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2053e1f50472a9fed67d4c84d9cb938.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc335ee14fc0b1130900cb82bcb3061.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8d09b9fc9719ff6faf32254b9d48713.png)
A.①与②的假设都错误 | B.①与②的假设都正确 |
C.①的假设正确,②的假设错误 | D.①的假设错误,②的假设正确 |
您最近一年使用:0次
2018-07-12更新
|
760次组卷
|
9卷引用:【全国市级联考】福建省三明市2017-2018学年高二下学期期末考试数学(文)试题
【全国市级联考】福建省三明市2017-2018学年高二下学期期末考试数学(文)试题湖北省咸宁市2018-2019学年高二下学期期末数学(文)试题黑龙江省大庆实验中学2021届高三得分训练(二)数学(理)试题安徽省宣城市郎溪中学2020-2021学年高二下学期第一次月考理科数学试题四川省仁寿第一中学校北校区2020-2021学年高二6月期末数学(文)试题广西河池市九校2020-2021学年高二下学期第二次联考数学(理)试题(已下线)考点43 直接证明与间接证明-备战2022年高考数学(理)一轮复习考点微专题(已下线)数学(上海B卷)河南省灵宝市第五高级中学2021-2022学年高二下学期第一次月考数学文科试题
名校
7 . 已知
,我们知道
成立.
(1)求证:
;
(2)同理我们也可以证明出
.由上述几个不等式,请你猜测一个与
和
有关的不等式,并用数学归纳法证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81cbab062d7c2b918dca90e9e92682f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4df660da8b095ea86e010d54080be614.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47b2e22d798a51902cbfd62a24641009.png)
(2)同理我们也可以证明出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c9b07fd25b6e44656f6b186c7bb6915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a83ebbc345b194f2a9063d8e10e40672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5da2c6ead4d33e9a602dc85bd55c598.png)
您最近一年使用:0次
2017-06-27更新
|
296次组卷
|
3卷引用:福建省三明市第一中学2016-2017学年高二下学期第二次月考数学(理)试题
福建省三明市第一中学2016-2017学年高二下学期第二次月考数学(理)试题(已下线)专题12.2 直接证明与间接证明、数学归纳法(精练)-2021年高考数学(理)一轮复习讲练测陕西省西安市第一中学2020-2021学年高二下学期期中理科数学试题
8 . 如图,已知三棱锥
中,
,D为
中点,
为
的中点,且
.
![](https://img.xkw.com/dksih/QBM/2011/12/6/1570558621270016/1570558626742272/STEM/69794df487414bdab306d2c63120480b.png?resizew=217)
(I)求证:
面
;
(II)找出三棱锥
中一组面与面垂直的位置关系,并给出证明(只需找到一组即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036de574712cad14bddadf6653c7e714.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](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/2680fc712ba2729a5ebbeb6ff9633047.png)
![](https://img.xkw.com/dksih/QBM/2011/12/6/1570558621270016/1570558626742272/STEM/69794df487414bdab306d2c63120480b.png?resizew=217)
(I)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70364f7ba745daf15c2d638298503acd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(II)找出三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
9 . 设M是由满足下列条件的函数
构成的集合:“①方程
有实数根;②函数
的导数
满足
”.
(1)判断函数
是否是集合M中的元素,并说明理由;
(2)若集合M中的元素具有下面的性质:“若
的定义域为D,则对于任意
,都存在
,使得等式
成立”,试用这一性质证明:方程
只有一个实数根;
(3)设
是方程
的实数根,求证:对于
定义域中的任意的
,当
且
时,
.
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/ae69ca2dbf214361aaced19128f5b3ad.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/6021540f69a449d888b651a72c1479ef.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/ae69ca2dbf214361aaced19128f5b3ad.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/03232f0551f6467eac414c60d35586a1.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/9779437256ef4567a6622615f573e146.png)
(1)判断函数
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/abb75ec4ca244cb6acf77767c9e2801f.png)
(2)若集合M中的元素具有下面的性质:“若
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/ae69ca2dbf214361aaced19128f5b3ad.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/26bee806fbe340b69bb98cea2c4a27c1.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/9fe616bad37a46349490cadbc5d6eb0d.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/5f915debb4c64765aa8217365ab3ec4e.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/6021540f69a449d888b651a72c1479ef.png)
(3)设
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/666cf56f0d7547ef82a6ccd8c59ca96d.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/6021540f69a449d888b651a72c1479ef.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/ae69ca2dbf214361aaced19128f5b3ad.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/4407e7eea4b74ec884317d371fa5fd39.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/bf69921ad4954c8cb68344594560c1cb.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/0509a1f80c6e464e8b90705c0e053bb3.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570006047989760/1570006053412864/STEM/25d2084c3eb94f33935b3390721b5274.png)
您最近一年使用:0次
13-14高二下·福建三明·期中
10 . 已知函数
是
上的增函数.
(1)若
,且
,求证
;
(2)判断(1)中命题的逆命题是否成立,并证明你的结论.
![](https://img.xkw.com/dksih/QBM/2016/11/29/1573186126700544/1573186133049344/STEM/b53443865f9b40ebbec63919508c6e49.png)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1573186126700544/1573186133049344/STEM/a4bd4f4388c24bebb08908c9ae452547.png)
(1)若
![](https://img.xkw.com/dksih/QBM/2016/11/29/1573186126700544/1573186133049344/STEM/73c4b5be20ae45869835a8219f58f908.png)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1573186126700544/1573186133049344/STEM/bcc104d6af0b4990a16b4ed625ba0494.png)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1573186126700544/1573186133049344/STEM/6b931602181d430398881761b853fd51.png)
(2)判断(1)中命题的逆命题是否成立,并证明你的结论.
您最近一年使用:0次
2016-12-03更新
|
2604次组卷
|
3卷引用:2013-2014学年福建省三明一中高二下学期期中考试文科数学试卷