解题方法
1 . 设
,
.如果存在
使得
,那么就说
可被
整除(或
整除
),记做
且称
是
的倍数,
是
的约数(也可称为除数、因数).
不能被
整除就记做
.由整除的定义,不难得出整除的下面几条性质:①若
,
,则
;②
,
互质,若
,
,则
;③若
,则
,其中
.
(1)若数列
满足,
,其前
项和为
,证明:
;
(2)若
为奇数,求证:
能被
整除;
(3)对于整数
与
,
,求证:
可整除
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72ea8ec0d9f8b1cfc4de834b8bfb608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87803b7cee18366b89d51799250df510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6705dba65746e1d4cac6a268b3c806ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/020e12ff4f028aba3a205a95e650d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79bda3d07c2fef4d6af4a13ade4c743e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020e12ff4f028aba3a205a95e650d72b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d6df2a57b7e5be32c05c10257ea6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91638bacbf4d15736d26713ba90e0fc4.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/91638bacbf4d15736d26713ba90e0fc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d6df2a57b7e5be32c05c10257ea6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0601879ae4ca9592246d135bfa48658c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383eb235f8e0ceda13367b16d29e0180.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503618b9bfb53a06f0ec6a5e427dcdbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0da20edf2714109dcfded7e212ec44a.png)
(1)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e12059d1dac926a235ccd40c3b61b1b6.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/ed9dbd8ed61db4f1c14f6b0e5f071200.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e1e4de97f8490fddcff16afe8583266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
(3)对于整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b96cdd9e003120b6102d927dbf53e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5009ce2d56180d31204f77c871fb375c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b326965628b5d967aafe9e696fdc07.png)
您最近一年使用:0次
2 . 固定项链的两端,在重力的作用下项链所形成的曲线是悬链线.1691年,莱布尼茨等得出“悬链线”方程
,其中
为参数.当
时,就是双曲余弦函数
,类似地我们可以定义双曲正弦函数
.它们与正、余弦函数有许多类似的性质.
(1)类比正弦函数的二倍角公式,请写出双曲正弦函数的一个正确的结论:
_____________.(只写出即可,不要求证明);
(2)
,不等式
恒成立,求实数
的取值范围;
(3)若
,试比较
与
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852665ec9c3a65b758898059361f11a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a7c1d3681898e25187a896aeb0c8c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0718c04bdf70989bcc90b902671a692.png)
(1)类比正弦函数的二倍角公式,请写出双曲正弦函数的一个正确的结论:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d8fe1e65b09697538d4dee0746846f4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe9f3099ed9429dc5b4e38a350e524a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343e7c30c2a5d166819b28e23fad2203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/563f464c94feac28033f6f3a271fbe8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2cebaab3423dfb2f2c944dfc43df8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb966b7b2dd6581640bcee2d97dacf77.png)
您最近一年使用:0次
2024-01-27更新
|
945次组卷
|
9卷引用:福建省宁德市2023-2024学年高一上学期1月期末质量检测数学试题
福建省宁德市2023-2024学年高一上学期1月期末质量检测数学试题重庆市缙云教育联盟2024届高三下学期2月月度质量检测数学试题(已下线)压轴题函数与导数新定义题(九省联考第19题模式)讲河南省名校联盟2023-2024学年高一下学期3月测试数学试题(已下线)第八章:向量的数量积与三角恒等变换章末重点题型复习(2)-同步精品课堂(人教B版2019必修第三册)河南省信阳市信阳高级中学2023-2024学年高一下学期3月月考(一)数学试题(已下线)第8章:向量的数量积与三角恒等变换章末综合检测卷(新题型)-【帮课堂】(人教B版2019必修第三册)(已下线)专题04 三角函数恒等变形综合大题归类 -期末考点大串讲(苏教版(2019))(已下线)专题08 期末必刷解答题专题训练的7种常考题型归类-期末真题分类汇编(北师大版2019必修第二册)
名校
解题方法
3 . 悬索桥(如图)的外观大漂亮,悬索的形状是平面几何中的悬链线.
年莱布尼兹和伯努利推导出某链线的方程为
,其中
为参数.当
时,该方程就是双曲余弦函数
,类似的我们有双曲正弦函数
.
![](https://img.xkw.com/dksih/QBM/2022/1/23/2900721970536448/2907279254913024/STEM/8a914e2499134cf68207c8add767fe65.png?resizew=325)
(1)从下列三个结论中选择一个进行证明,并求函数
的最小值;
①
;
②
;
③
.
(2)求证:
,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/046db679c09a10434e81f7a01c55e243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ad2f5a11d7437f506adab0996961269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0099b9b80ed478824fa95677ebe9d5b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3321510a9eb73909a36c084a8630e89.png)
![](https://img.xkw.com/dksih/QBM/2022/1/23/2900721970536448/2907279254913024/STEM/8a914e2499134cf68207c8add767fe65.png?resizew=325)
(1)从下列三个结论中选择一个进行证明,并求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3634cf0ca04b381dec8fcfee8805bdac.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff61bdd9ed784248cfdcc965ce06db0.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e40ff30f6f7fca28159dedeff7168c74.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c3de984177769fa426e10eb14cd82c.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0645c3c42e19271f86a10b1fe9dbb0f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b39ee39c38f49390a03be161109a2b4.png)
您最近一年使用:0次
2022-02-01更新
|
1295次组卷
|
7卷引用:江苏省苏州市2021-2022学年高一上学期期末数学试题
江苏省苏州市2021-2022学年高一上学期期末数学试题湖南省株洲市第二中学2021-2022学年高一下学期“同济大学”杯数理化联赛数学试题重庆市2023届高三下学期3月月度质量检测数学试题湖南省株洲市南方中学2022-2023学年高一下学期期末数学试题(已下线)重难点突破02 函数的综合应用(九大题型)(已下线)压轴题函数与导数新定义题(九省联考第19题模式)讲(已下线)压轴题三角函数新定义题(九省联考第19题模式)讲
解题方法
4 . 微分中值定理是微积分学中的重要定理,它是研究区间上函数值变化规律的有效工具,其中拉格朗日中值定理是核心,它的内容如下:
如果函数
在闭区间
上连续,在开区间
可导,导数为
,那么在开区间
内至少存在一点
,使得
,其中
叫做
在
上的“拉格朗日中值点”.已知函数
.
(1)若
,求函数
在
上的“拉格朗日中值点”
;
(2)若
,求证:函数
在区间
图象上任意两点
,
连线的斜率不大于
;
(3)若
,且
,求证:
.
如果函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f3fcc5073759c73c7a63c8818eca5c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d11582cafaca7560189cf57e70f6a46d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58423a31ef72d8d161b775090c9ed2c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bcc88c47bbbace2c56adced4f781b6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d0d09c61ed9d7289d948d2ab559657f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.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/25a9a2cda21bc7d84330702878e61c63.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1dffe15ea2b4735ad2a274144301328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098345d96f648ba45ad923a79e815496.png)
您最近一年使用:0次
5 . 复平面是人类漫漫数学历史中的一副佳作,他以虚无缥缈的数字展示了人类数学最纯粹的浪漫.欧拉公式可以说是这座数学王座上最璀璨的明珠,相关的内容是,欧拉公式:
,其中
表示虚数单位,
是自然对数的底数.数学家泰勒对此也提出了相关公式:
其中的感叹号!表示阶乘
,试回答下列问题:
(1)试证明欧拉公式.
(2)利用欧拉公式,求出以下方程的所有复数解.
①
;②
;
(3)求出角度
的
倍角公式(用
表示,
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5aa584db159b0f9bfae801d0134393b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/574f94ac7dfd3477b58799e0251bb6a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a260aee25664815506d2720174b03829.png)
(1)试证明欧拉公式.
(2)利用欧拉公式,求出以下方程的所有复数解.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bde2a8df1f0418c41a6e077c7f5de21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1150e58bbcb15a349fb5b9b5ef708d41.png)
(3)求出角度
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9d7bbcbeb05fbbb06463120f9a6811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8cd112c1cb203187e3c9554617c45b8.png)
您最近一年使用:0次
名校
解题方法
6 . 三等分角是古希腊几何尺规作图的三大问题之一,如今数学上已经证明三等分任意角是尺规作图不可能问题,如果不局限于尺规,三等分任意角是可能的.下面是数学家帕普斯给出的一种三等分角的方法:已知角
的顶点为
,在
的两边上截取
,连接
,在线段
上取一点
,使得
,记
的中点为
,以
为中心,
为顶点作离心率为2的双曲线
,以
为圆心,
为半径作圆,与双曲线
左支交于点
(射线
在
内部),则
.在上述作法中,以
为原点,直线
为
轴建立如图所示的平面直角坐标系,若
,点
在
轴的上方.
的方程;
(2)若过点
且与
轴垂直的直线交
轴于点
,点
到直线
的距离为
.
证明:①
为定值;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a998a7d4d980e848ee050b706480ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e587c886cd9f7d48f0cce82dcb940c8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75eb52879657138c23304b1634c73f7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf1438142deeac876fc7dc50552e552.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d566a90ab70e7133f0f110143a4f06ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5881b1640911274127b9aa3d647ee903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
证明:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422fd5f0bdef76f7f05c6f803dddc982.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d566a90ab70e7133f0f110143a4f06ae.png)
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7 . 南宋的数学家杨辉“善于把已知形状、大小的几何图形的求面积,体积的连续量问题转化为求离散变量的垛积问题”.在他的专著《详解九章算法·商功》中,杨辉将堆垛与相应立体图形作类比,推导出了三角垛、方垛、刍薨垛、刍童垛等的公式.如图,“三角垛”的最上层有1个球,第二层有3个球,第三层有6个球……第
层球数是第n层球数与
的和,设各层球数构成一个数列
.
的通项公式;
(2)证明:当
时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbad207743c20091cdc5e2114184a01.png)
(3)若数列
满足
,对于
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cbad207743c20091cdc5e2114184a01.png)
(3)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c1ecbdd820cb0c4945e124d29a2b9d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a37a59558292ad6b3d0978bfd7484990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2360a6dbfca8164cebf81fff5a7282.png)
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8 . 《九章算术》中,将底面为长方形且有一条侧棱与底面垂直的四棱锥称之为阳马,将四个面都为直角三角形的四面体称之为鳖臑.在如图所示的阳马
中,侧棱
底面ABCD,且
,点E是PC的中点,连接DE、BD、BE.
平面
.试判断四面体
是否为鳖臑.若是,写出其每个面的直角(只需写出结论);若不是,请说明理由;
(2)设H点是AD的中点,若面EDB与面ABCD所成二面角的大小为
,求四棱锥
的外接球的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a8067cc458cf12887177487c3cfb9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e1e4ea140260a790885868bc7a94f2.png)
(2)设H点是AD的中点,若面EDB与面ABCD所成二面角的大小为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc33a16c65cd1930cc5f7c887e4dccb9.png)
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9 . 若集合
的非空子集
满足:对任意给定的
,若
,有
,则称子集
是
的“好子集”.记
为
的好子集的个数.例如:
的7个非空子集中只有
不是好子集,即
.记
表示集合
的元素个数.
(1)求
的值;
(2)若
是
的好子集,且
.证明:
中元素可以排成一个等差数列;
(3)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f5c44de003475d3466981293cf5e47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/887982e3735dd7ca13293338a12df593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c469f6345826410959ea09d7e3192e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0586ec8d1d9796fb80a1250e2c0a4b0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38fcec7af3520884b173b29bda6c657a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b26bbb11e932ddb26a9088e7fc33e87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27c562f247c1d691158f4038a030574c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68eafd45c1ec4b414d3553dabd8c2848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37765d2927d24d4b582423c843aebcd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32a859898e9905e0524d3a982eb34b6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ada01c2a8b4d92df94834a6a3929673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79df6a6d73a058d13632a726c2308d66.png)
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解题方法
10 . 我国古代数学家赵爽为了证明勾股定理,创制了一副“弦图”.后人称其为“赵爽弦图”.如图,现提供5种颜色给图中的5个小区域涂色,规定每个区域只涂一种颜色,相邻区域颜色不相同.记事件
:“区域2和区域4颜色不同”,事件
:“所有区域颜色均不相同”,则
( )
![](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/36f2666380ef520111b6a1484f56372f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次