名校
1 . 已知数列
的通项为
,前
项和为
,则下列选项中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
A.如果![]() ![]() ![]() ![]() |
B.如果![]() ![]() ![]() ![]() |
C.如果![]() ![]() ![]() ![]() |
D.如果![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-05-21更新
|
949次组卷
|
3卷引用:湖北省黄石市第二中学2023-2024学年高三下学期三模考试数学试题
名校
2 . 已知平面上到定点
的距离与到定直线
:
的距离之比为常数
的点的轨迹为曲线
.
(1)求曲线
的方程;
(2)把曲线
及直线
都向左平移5个单位长度,得到曲线
及直线
,写出
及
的方程(只写出结果);
(3)若
,
是
上的两点,且
.直线
交直线
于点
,求直线
与直线
所成锐角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c1d8736a2f5a41c1942f8684ab3a81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35254a53dabcf0e63e437774ceaf417.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d59ab85c075a09d55d69e159e4abb268.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)把曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f5817ab7b88e9d8a83dd086ffdb3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f5817ab7b88e9d8a83dd086ffdb3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(3)若
![](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/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/660964e4c6710e01ba34521ad419c3ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963111aff6952322dfaca75ae069873c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
您最近一年使用:0次
3 . 已知椭圆
,圆
.
(1)点
是椭圆
的下顶点,点
在椭圆
上,点
在圆
上(点
异于点
),连
,直线
与直线
的斜率分别记作
,若
,试判断直线
是否过定点?若过定点,请求出定点坐标;若不过定点,请说明理由.
(2)椭圆
的左、右顶点分别为点
,点
(异于顶点)在椭圆
上且位于
轴上方,连
分别交
轴于点
,点
在圆
上,求证:
的充要条件为
轴.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f036026cd92e9ad059c3f22a7658638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b1cb1359bcb061ce7737fb7e1b34f1.png)
(1)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa154ac33703b5c836047b2143697c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0aea8e4a6e524f43f9a13c1ef4fbddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37f4fed042a050d47d7f1331605d7923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa0defb1d52e1973c1c6db736574dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c782675efb07943bcee0339945a08711.png)
您最近一年使用:0次
4 . 函数
与
之间的关系非常密切,号称函数中的双子座,以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0c0fb7d7810f3f95415e61621d07a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe8383def220f92d50af7cc60ad9c37.png)
A.若![]() ![]() ![]() ![]() |
B.![]() |
C.直线![]() ![]() |
D.若直线![]() ![]() |
您最近一年使用:0次
5 . 已知函数
.
(1)求函数
的单调区间;
(2)若函数
的两个极值点分别为
,证明:
;
(3)设
,求证:当
时,
有且仅有2个不同的零点.
(参考数据:
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d797a2db981447da3e604690da4afca.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dabb97b3033a9915c9016df81df91b94.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ade931035db1a9b2f6f96ab9133148b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd60e69dac32dc020aacf5df042e5f2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec068ca23b1226af6b27e20d57b87e9.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74517b26a5a02c30c94f031d52d63014.png)
您最近一年使用:0次
解题方法
6 . “对称性”是一个广义的概念,包含“几何对称性”、“置换对称性”等范畴,是数学之美的重要体现.假定以下各点均在第一象限,各函数的定义域均为
.设点
,
,
,规定
,且对于运算“
”,
表示坐标为
的点.若点U,V,W满足
,则称V与U相似,记作V~U.若存在单调函数
和
,使得对于
图像上任意一点T,
均在
图像上,则称
为
的镜像函数.
(1)若点
,
,且N~M,求
的坐标;
(2)证明:若
为
的镜像函数,
,则
;
(3)已知函数
,
为
的镜像函数.设R~S,且
.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6f5adf13b4214666292dd64b947741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf145ba1997cc3d08e33f293254e6f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af405a054bfe7fb7ce40e48d816467e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2795f6fc7043f930745976968466fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36e16415b61722f9961e412386e6819f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fde4ec543a9f0c90361dc745f44803d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e472c830f937c5b6d170697b57104d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3be375f2101d25d3cb0918bf65b682b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd2ac83d16c87fcc7056e4c6dbbff36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661249bf6499017f9e5e03db3fcd93d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643cf4c0177c40edaf01e676c1d54c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5083e04454a558782d3bcbd2cabdde26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd2ac83d16c87fcc7056e4c6dbbff36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2595e01e8751886a27862cce04e2d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b925f9f6da6b75ee413e4de5701855a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b7dad535985c70409e9c799c559386b.png)
(2)证明:若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e468e814daa94be212832da87ca2432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8569e7b5710b68a93b65b8930415b8eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9716315555c1c3facc71023e6e1c75b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/162768e1de8cab5e6e19b748a47b2216.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c945a45ca2e036019d017d2bec45d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8195f5ae98c4c40ff17aa510e39b46b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4ebc9e30c1977652e8b9bfd6f10dc14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd72ac36aedac2ba9271b332e59d33ce.png)
您最近一年使用:0次
7 . 设抛物线
,过点
的直线与
交于
两点,且
.若抛物线
的焦点为
,记
的面积分别为
.
的最小值.
(2)设点
,直线
与抛物线
的另一交点为
,求证:直线
过定点.
(3)我国古代南北朝数学家祖暅所提出的祖暅原理是“幂势既同,则积不容异”,即:夹在两个平行平面间的两个几何体被平行于这两个平面的任意平面所截,如果截得的两个截面的面积总相等,那么这两个几何体的体积相等.当
为等腰直角三角形时,记线段
与抛物线围成的封闭图形为
绕
轴旋转半周形成的曲面所围成的几何体为
.试用祖桓原理的数学思想求出
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c0eec43d5b63ea6473d4db55f6616d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bde7dffe15aab0af3f5163c231fb86d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/234c20c6349129e8fd64df13eb3368a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d354bb51cf265ad8412dd713c382dad8.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf2fa1e61446162d6db06ec48ed7a64f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(3)我国古代南北朝数学家祖暅所提出的祖暅原理是“幂势既同,则积不容异”,即:夹在两个平行平面间的两个几何体被平行于这两个平面的任意平面所截,如果截得的两个截面的面积总相等,那么这两个几何体的体积相等.当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5414ae4121af4ff378c33a956f17f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0047f659c182291c84c224df6b5e993f.png)
您最近一年使用:0次
8 . 已知椭圆
的右焦点为
,其四个顶点的连线围成的四边形面积为
;菱形
内接于椭圆
.
(1)求椭圆
的标准方程;
(2)(ⅰ)坐标原点
在边
上的投影为点
,求点
的轨迹方程;
(ⅱ)求菱形
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41322821ce31416fdac8dd6e0aa41c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)(ⅰ)坐标原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(ⅱ)求菱形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
您最近一年使用:0次
9 . 若函数
的图象上的两个不同点处的切线互相重合,则称该切线为函数
的图象的“自公切线”,称这两点为函数
的图象的一对“同切点”.
(1)分别判断函数
与
的图象是否存在“自公切线”,并说明理由;
(2)若
,求证:函数
有唯一零点且该函数的图象不存在“自公切线”;
(3)设
,
的零点为
,
,求证:“存在
,使得点
与
是函数
的图象的一对‘同切点’”的充要条件是“
是数列
中的项”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf5beca5f1a475dbf003bb2e27d51dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf5beca5f1a475dbf003bb2e27d51dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf5beca5f1a475dbf003bb2e27d51dd.png)
(1)分别判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2750eb2ffdae5d0be38bda2ebb51875b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c6e387dd234bb49f53df1668d5e63e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4157d7a3d18b13df5428790499406f7d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039124ad765f2a9d8d3382bdc60a3d6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3282e5fde4ae53fcb1bb072a685304c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1551e58c685b32149bffcb9329e710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdab40c21646025ac21019cf6e883c54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a943c3df48c0961838d083e1c34fdbdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fa720a5bafa2bb6ec5c60197e74a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2b9643da0c0fea4f099f9a9133d6076.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d2fad3eba14b645100f279cf2af2ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086e9b14c35ef3c57b20f5e952ebf9c8.png)
您最近一年使用:0次
名校
解题方法
10 . 已知双曲线
的两条渐近线分别为
和
,右焦点坐标为
为坐标原点.
(2)直线
与双曲线的右支交于点
(
在
的上方),过点
分别作
的平行线,交于点
,过点
且斜率为4的直线与双曲线交于点
(
在
的上方),再过点
分别作
的平行线,交于点
,这样一直操作下去,可以得到一列点
.
证明:①
共线;
②
为定值
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4073d527d4b14759a7cbaeabfb35a756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9fc68d6d88485e65bfc599dfdde547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c388c5a37852ee8ea1066ce1f9c1d5dd.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81337e2e2dbdd0c3148454fa41d44144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8454989732716850cb57ca15f8ef596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8454989732716850cb57ca15f8ef596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c7d2c85e7878b6cbfb45b71ffb60b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ee712dfc82e1acc31ef8dcad479a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ee712dfc82e1acc31ef8dcad479a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c7d2c85e7878b6cbfb45b71ffb60b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ca7a25d804f483ec024c735c633e62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8357bec2e11a9f9756cd7c7e9143afca.png)
证明:①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db4fe79b98486f0d4556f37d64d74f9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeda3264e04e2d3ed2a15c69adad05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47dd9cb5cac04bc15c02f292b38d2928.png)
您最近一年使用:0次
2024-05-08更新
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486次组卷
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3卷引用:河南省部分重点高中2023-2024学年高三下学期5月大联考数学试题