1 . 已知函数
.
(1)证明:
;
(2)设
,求证:对任意的
,都有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bba0b8ca5aeae32b8a8c03123ae2f65.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa662f0273f0921c1fa4727f632395.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29b7c58e271f5931c127f2caf572a261.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7fee6e7b28e3954a3130a37b2a0a38e.png)
您最近一年使用:0次
名校
解题方法
2 . 记数列
的前n项和为
,对任意正整数n,有
,且
.
(1)求
和
的值,并猜想
的通项公式;
(2)证明第(1)问猜想的通项公式;
(3)设
,数列
的前n项和为
,求证:
.
![](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/b75814bf9729ad275e599944cfce6bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2693734765399876e9e93cdb110231c4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明第(1)问猜想的通项公式;
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c64d46ff2bbfba2902ef2f4193295903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebdf072477557ad3dbc7acfa8088436d.png)
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名校
解题方法
3 . 已知数列
中,
,数列
的前n项和
满足:
.
(1)证明;数列
是等比数列,并求通项公式
;
(2)设
,且数列
的前n项和
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039e4fe671d61e59b96ee525c9df43e8.png)
![](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/2522ffd3ef2c1b8794921cee883e091d.png)
(1)证明;数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e2de706dc5f0439b989273a5367f63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94e22de952e2b63bb9a750a77200d77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50048f2ab3c89aa1dd2ddb75df35b47f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c215db1d8f69757118ad405b78035628.png)
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4 . 对于项数为
的数列
,若数列
满足
,
,其中,
表示数集
中最大的数,则称数列
是
的
数列.
(1)若各项均为正整数的数列
的
数列是
,写出所有的数列
;
(2)证明:若数列
中存在
使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce3b6654490dcd8177970631e929d3d.png)
,则存在
使得
成立;
(3)数列
是
的
数列,数列
是
的
数列,定义
其中
.求证:
为单调递增数列的充要条件是
为单调递增数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb951647594b67c82045b7ba69f57cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3bd239656c2ef509ed9f2a91a68317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd88e35dc6c2b82b4bb29475d37c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cda05b106f920bbcfa02320229ca3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/698f45c9ed5bb04924f1037107e76988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3bd239656c2ef509ed9f2a91a68317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb951647594b67c82045b7ba69f57cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)若各项均为正整数的数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb951647594b67c82045b7ba69f57cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2f32a17f0261d32079efed31d414a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb951647594b67c82045b7ba69f57cd.png)
(2)证明:若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb951647594b67c82045b7ba69f57cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce3b6654490dcd8177970631e929d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afadbd5dc4d8003ac2a0c85678dbecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4578089af6806bf1257491091b924d3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2dd6a827492dffddd07e621a4bbe36.png)
(3)数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3bd239656c2ef509ed9f2a91a68317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb951647594b67c82045b7ba69f57cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4af75cc7d8cc976dce8bf9bd8fdc18f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa9f328d5108bbec5c56eebfe95567.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d019d9549df6aed0dab378301d889ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70322214e5c9d9a8df10eb45930f5745.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb2e86a5aa896bef041701e0e1771ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8504784fec514a92d845910c6721c3a.png)
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5 . 已知数列
的首项
,且满足
.
(1)求证:数列
为等比数列;
(2)记
,求数列
的前
项和
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86fc336b4a83bf6d66c4afcc431597f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56427ad67adeb058f8d1cfcb48a73a84.png)
(1)求证:数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c895d4ce5ce82ef9b311b9369b4de11.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88199a83552b38875bdefc71f71f728e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15582954846624184078807b41bbbdef.png)
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2023高二上·上海·专题练习
解题方法
6 . 叙述并证明三垂线定理(要求写出已知、求证、证明过程并画图);
您最近一年使用:0次
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解题方法
7 . 已知函数
,
.
(1)若函数
在R上单调递减,求a的取值范围;
(2)已知
,
,
,
,求证:
;
(3)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d013335d41c7a1e51b381eb8e7ef977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111870a9ef48f1bb2797ae8f1825a8f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9897559d21ef1971f497be4269b107aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0527a896aec4a245945e5edee00deed.png)
(3)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f6bf190c55c3a0ddbca2ff7a5ecf42.png)
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2023-12-30更新
|
1117次组卷
|
3卷引用:吉林省通化市梅河口市第五中学2023-2024学年高二下学期第一次月考数学试题
名校
8 . 如图,在三棱柱
中,平面
平面
,
边长为8的正方形,
.
(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/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9fe42fb1a9602d9881331f705217eca.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/10/55df57a7-4449-4f47-9d6f-53c336209693.png?resizew=131)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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)
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解题方法
9 . 如图,在棱长均相等的平行六面体
中,用空间向量证明下列结论.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/05306c01-ff12-46a1-9020-d04c04d1978b.png?resizew=173)
(1)若
,求证:
平面
;
(2)若
是棱
的中点,
是
上靠近点
的三等分点,求证:
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/05306c01-ff12-46a1-9020-d04c04d1978b.png?resizew=173)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9c4adb05045cdd808a1ff7d6662d79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637bdc8cf5c522d2abab727ec3a11631.png)
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10 . (1)证明“直线与平面垂直的判定定理”:如果一条直线与一个平面内的两条相交直线垂直,则该直线与此平面垂直.
已知:如图,
,
,
,
.求证:
;
![](https://img.xkw.com/dksih/QBM/2023/11/17/3369796464435200/3370169716801536/STEM/653a2bc095e040b2a0c772ff8704c289.png?resizew=130)
(2)证明:平行四边形两条对角线的平方和等于两条邻边的平方和的两倍.
如图,四边形
是平行四边形.求证:
.
已知:如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6182bd53bccdad13334835221362a4d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60750b5eab6344496e925eb603cab46a.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)
![](https://img.xkw.com/dksih/QBM/2023/11/17/3369796464435200/3370169716801536/STEM/653a2bc095e040b2a0c772ff8704c289.png?resizew=130)
(2)证明:平行四边形两条对角线的平方和等于两条邻边的平方和的两倍.
如图,四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7105465941e9c130703b15790c6c1ecf.png)
![](https://img.xkw.com/dksih/QBM/2023/11/17/3369796464435200/3370169716801536/STEM/35d2213ed5264d45abd83c78d2631c9a.png?resizew=141)
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