名校
解题方法
1 . 在
中,角
所对的边分别是
,若
是
边上的一点,且
.
(1)若
时,求
面积的最大值;
(2)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d319424e5bd9c657b252d5edde7a9b79.png)
①求角
的大小;
②当
取得最大值时,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7af7c5df749c6fa9bbe87faa72c66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f2599ca8b6b683e57a82699c8b1ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c13377d1b9792367317b4cd0a8242eec.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c42206023d239aa78646e76fa7cb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d319424e5bd9c657b252d5edde7a9b79.png)
①求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4231aebdebd43211cdeb5cf0db6f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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名校
解题方法
2 . 一个棱长为2的正四面体盒子内部放置了一个正方体,且该正方体在铁盒内能任意转动,则该正方体棱长的最大值为_______ .
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名校
3 . 已知复数
,则下列说法不正确的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e2c56730cc80b233be20a1ab17ad38.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 1712年英国数学家布鲁克·泰勒提出了著名的泰勒公式,该公式利用了多项式函数曲线来逼近任意一个原函数曲线,该公式在近似计算,函数拟合,计算机科学上有着举足轻重的作用.如下列常见函数的
阶泰勒展开式为:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf4a87ad1e9742f47b0c5b44b8dfab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b113d94079c4b2138c2325e1141c5bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1557366a2ea0c602935e5da8fb495d6.png)
其中
,读作
的阶乘.
1748年瑞士数学家莱昂哈德·欧拉在泰勒公式的灵感下创造了人类数学最美妙的公式,即欧拉公式
,特别的欧拉恒等式
被后世称为“上帝公式”.欧拉公式建立了复数域中指数函数与圆函数(正余弦函数)的关系,利用欧拉公式还可以完成圆的
等分,即棣莫弗定理
的应用.
(1)请写出复数
的三角形式,并利用泰勒展开式估算出
的3阶近似值(精确到0.001);
(2)请根据上述材料证明欧拉公式,并计算
与
;
(3)记
,由棣莫弗定理得
,从而得
,复数
,我们称其为1在复数域内的三次方根. 若
为64在复数域内的6次方根.求
取值构成的集合,其中
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf4a87ad1e9742f47b0c5b44b8dfab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b113d94079c4b2138c2325e1141c5bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1557366a2ea0c602935e5da8fb495d6.png)
其中
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/815fbba8af7b1ecfb112be6b04284191.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
1748年瑞士数学家莱昂哈德·欧拉在泰勒公式的灵感下创造了人类数学最美妙的公式,即欧拉公式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26032c72018539ca7aa3ca66ac845260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8998724d22d1f99493dd285a9e5bfe63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419e0831142916b945a1c1004c7cd6c5.png)
(1)请写出复数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7a56b5b169d5ecff40690f5def68e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
(2)请根据上述材料证明欧拉公式,并计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e5bebae7756550f899bbc18ea8bc923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8dfbd1655b2e4b2c629b2e77fc3e7f06.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd0c30155ec5bc576f72e97afc42abaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a606f335bfbfabc3362b1faf49add59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0555a4bd63bc674ceca48ba08c4023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c88c2ca3f32231770665622da3ba4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb85abfc312eb4ac4cd1321b033f328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78488089f169e8222beb6cdb772af3d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c83f84dad2257eeb8fd3c6c38c671b.png)
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名校
解题方法
5 . 已知向量
满足:
为单位向量,且
与
相互垂直,又对任意
不等式
恒成立,若
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23c5d7ba714351d679bbbb287af5aaec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83c5803cc8c05849028a57c4bd4ee72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a06c8eae3652486cf9e416ce3a8ffc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d89edb09a343c23e415b3e7d8fd837b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac6ef8c5afe13c4a6a1eb67086f11d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0719bceff0114835c72cb6e25831d04c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83634e314df24df73ae37d25a44d20e3.png)
A.4 | B.5 | C.6 | D.7 |
您最近一年使用:0次
名校
解题方法
6 . 在
中,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3014842cc5f4e9c6a5d9ecef27e1bc6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f8c53f43770c0d22fcbcd771a933fde.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024高三·天津·专题练习
7 . 已知
,
,
分别为
三个内角
,
,
的对边,且
.
(1)求
;
(2)若
,求
的值;
(3)若
的面积为
,
,求
的周长.
![](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/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/229ebff0c9f6d0838d9ceaa5f59754e4.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5321ef782f50670b895f93bf08b61b98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89d66e84de508cfdeefea262bff0adcf.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bbb86e88765213f7b00d9962d56941e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2024-04-10更新
|
2136次组卷
|
4卷引用:重庆市万州区万州第一中学2023-2024学年高一下学期3月月考数学试题
重庆市万州区万州第一中学2023-2024学年高一下学期3月月考数学试题河北省廊坊市文安县第一中学2023-2024学年高一下学期第一次集中练(3月月考)数学试题(已下线)专题11.2正弦定理-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)黄金卷06
名校
解题方法
8 . 在
中,角
所对的边分别是
,下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
A.若![]() ![]() |
B.若![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() |
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2024-04-04更新
|
481次组卷
|
3卷引用:重庆市万州二中教育集团2023-2024学年高一下学期期中考试数学试卷
名校
解题方法
9 . 已知
:向量
与
的夹角为锐角.若
是假命题,则实数
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4d143a19cf7adcbf5c6bd5c1213edd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2ba55b52e1546e97eefc527257873fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-04-01更新
|
1068次组卷
|
5卷引用:重庆市万州区万州第一中学2023-2024学年高一下学期3月月考数学试题
名校
解题方法
10 . 在
中,点
在边
上,且
.点
满足
.若
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7289ef8051c49b4089836bac6f70b4d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9415cc568e6ad9e838a6f3c5f5c920a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6060d9a82ed5405a1ea8cd824448b6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d585633bffdf031ee5c67ec29f51667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3ac010cc1c8a6ecad23d26dc7cc2b61.png)
A.![]() | B.![]() | C.12 | D.11 |
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|
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