名校
解题方法
1 . 已知数列
满足
,
,
,
成等差数列.
(1)求证:数列
是等比数列,并求出
的通项公式;
(2)记
的前n项和为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2438f2272d7b7ab51dbbe587025a553d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479c0564241789f8f52ac4fda26e9904.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6197e2365d7f39507f8671acfc25a339.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213e22890204937a5dded4436369390f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef130855c8dc1accbff28762858f20bf.png)
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2024-06-09更新
|
542次组卷
|
2卷引用:江西省赣州市2023-2024学年高三下学期5月适应性考试数学试题
名校
解题方法
2 . 若函数
在定义域内存在两个不同的数
,
,同时满足
,且
在点
,
处的切线斜率相同,则称
为“切合函数”.
(1)证明:
为“切合函数”;
(2)若
为“切合函数”(其中
为自然对数的底数),并设满足条件的两个数为
,
.
(ⅰ)求证:
;
(ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.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/abf7c745cd02f4620a175cf00ec85e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24a2c53e3b0b1c08803e95419f909d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecaca8409b3f51d22667a14559c58ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe0de54dfc96a2291e8d5e56676eabc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb46178ba0560d96bd3a05891505b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c20b8bd265b07dd90690ad4e349c6dc.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cde09c609543feedc2e0c11992b2bd.png)
您最近一年使用:0次
2024-01-03更新
|
1036次组卷
|
4卷引用:江西省赣州市南康中学2024届高三上学期新高考“七省联考”考前数学猜题卷(一)
江西省赣州市南康中学2024届高三上学期新高考“七省联考”考前数学猜题卷(一)重庆市南开中学校2024届高三上学期第五次质量检测数学试题重庆市沙坪坝区南开中学校2024届高三上学期第五次质量检测数学试题(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编
3 . 求证:
.证明:因为
和
都是正数,所以为了证明
,只需证明
,展开得
,即
,只需证明
.因为
成立.所以不等式
成立.上述证明过程应用了( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564b3f0440d047ffdd641fb56974355b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f499828bdc14df52f0427a78ef51cc5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7782200f8eab2b9add12b2a99b6a03b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564b3f0440d047ffdd641fb56974355b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0825879cdd8323b3ff48e311aade56fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6be8f4788729fba5529f31660268e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef35b7c74b6e11ee179054fd7bdba3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d6e82ca711596894dedbe1896471ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d6e82ca711596894dedbe1896471ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/564b3f0440d047ffdd641fb56974355b.png)
A.综合法 | B.分析法 | C.反证法 | D.间接证法 |
您最近一年使用:0次
名校
4 . (1)已知
,比较
与
的大小,试将其推广至一般性结论(不需证明);
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/033e647fa068419afab6c99f2b6c062d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41ca3d6990c78af1743eeacad3cc782e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f781fa116cc0af5da62692e7a95da1.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0f1411c809779e524b3b52cdbcd178.png)
您最近一年使用:0次
名校
5 . 如图,在三棱柱
中,
是正方形,
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/934c8eca-7e7e-4595-af4f-1c5aa073e3f2.png?resizew=121)
(1)求证:
平面
;
(2)求二面角
的余弦值;
(3)证明:在线段
上存在点
,使得
,并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/934c8eca-7e7e-4595-af4f-1c5aa073e3f2.png?resizew=121)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8197bf06d017950c85c3ba6a291c095e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e2f7554a52815bfa0f4d75221ba7397.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95183b555d54b3a09ac20e9dcacb02ec.png)
(3)证明:在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84a436704964dc76f16c2c23665ab3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c04c68f1ef1e37534b5bbc7a1f592ef7.png)
您最近一年使用:0次
2021-11-19更新
|
479次组卷
|
4卷引用:江西省信丰中学2021-2022学年高二下学期第一次月考数学(理)B层试题
名校
6 . 在用数学归纳法证明“已知
,求证f(2n)<n+1”的过程中,由K推导K+1时,原式增加的项数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccdbf34750d455a43ee67f27c4f8e62b.png)
A.1 | B.K+1 | C.2K-1 | D.2K |
您最近一年使用:0次
2021-08-16更新
|
70次组卷
|
3卷引用:江西省兴国县第三中学2020-2021学年高二下学期第一次月考数学(理)(兴国班)试题
江西省兴国县第三中学2020-2021学年高二下学期第一次月考数学(理)(兴国班)试题(已下线)考点27 数学归纳法-备战2022年高考数学一轮复习考点帮(浙江专用)陕西省榆林市绥德中学2021-2022学年高二下学期第一次阶段性测试理科数学试题
7 . (1)证明:
;
(2)已知:
,
,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734f585f8cfc92522f6daf997ebec04d.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/a945b19a5442a7edfa8d0f1d4ef488da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b3eeae9616ea62a988bde7a82ddc98.png)
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2021-05-28更新
|
496次组卷
|
4卷引用:江西省赣州市赣县第三中学2021-2022学年高二4月月考数学(文)试题
名校
8 . (1)已知
,且
证明![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
(2)已知
是正实数,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a93645a9c1f5a2961519d74bf51567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e906ec0f947d031f8f426272176e7753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135125d796a469155fc4a22dc6be3d10.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d701d16d9f318ee8fa779f5b961d64c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3095b59b062a298fb3c4a9c45f57d9.png)
您最近一年使用:0次
2020-10-23更新
|
212次组卷
|
2卷引用:江西省赣州市定南中学2021-2022学年高二5月月考数学(文)试题
9 . 如图,在多面体
中,
为等边三角形,
,
,
,点
为边
的中点.
平面
.
(2)在
上找一点
使得平面
平面
,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f86652f9864f608ce96b993d196386ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af620f6d204d310d8e3f267fdd6c3f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ee81b6066188abee9d167b6c7f3f71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d46554105150391e671609fc6348a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678b28fddb166d90878d24d6e5481080.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53238eab89f2e272985b24e4cbdb5397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422210c777ac0d625bbd81cc7601bf9b.png)
您最近一年使用:0次
2020-01-03更新
|
812次组卷
|
7卷引用:江西省赣州市赣县第三中学2021-2022学年高一5月月考数学试题
名校
10 . 如图,在四棱锥
中,
是等腰三角形,且
.四边形
是直角梯形,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2018/11/2/2066738188689408/null/STEM/1f42a6ad68474dff984f89d4c313d642.png?resizew=153)
(Ⅰ)求证:
平面
;
(Ⅱ)当平面
平面
时,求四棱锥
的体积;
(Ⅲ)请在图中所给的五个点
中找出两个点,使得这两点所在的直线与直线
垂直,并给出证明 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f409b28f7cb97726646e79709ad25190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c4c15c36855da900d07c03d12fd7c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/729d5cb74bb927aa549ce596a35b26b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c90a2e13488a5f4a2408718837fdabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b36a1938df65db2b68bf7595b97bafa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac943d8c2eb91c0082ada87857d1ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd880e197a74294650d90579563a7b8.png)
![](https://img.xkw.com/dksih/QBM/2018/11/2/2066738188689408/null/STEM/1f42a6ad68474dff984f89d4c313d642.png?resizew=153)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7178236b6fadcce9a5cae9ef80146f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda09fb28b8f1e165715cca61d64f9c1.png)
(Ⅱ)当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/840798a31aba0783f96584e0ad7c0d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
(Ⅲ)请在图中所给的五个点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fd6e7723730c9b701d9b48a23e290dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
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