名校
1 . 初中学过多项式的基本运算法则,其实多项式与方程的根也有密切关联.对一组变量
,幂和对称多项式
,且
;初等对称多项式
表示在
中选出
个变量进行相乘再相加,且
.例如:对
.已知三次函数
有3个零点
,且
.记
,
.
(1)证明:
;
(2)(i)证明:
;
(ii)证明:
,且
;
(3)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74b85069b184b032808ce05636373b63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d15873316d0c17fbcbbe376834e5697.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b63239fb9313458d7f86b64d2860beba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba0d57c2c8fcc1cef3a02b67d4193b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca373f163399198a6beb169fe6df5262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aef4ab1ca44d62d6451f85e41258abe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c5f85f6501033a93c8be7363d59c8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489340c9a2d70c00bae13b7018cad448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93e7bb2538cf1dcb50722aa9cf0550c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a38c64a6143b210aa315e0b6bfaccf94.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e856070d58b6aefce7e914426d7f95c.png)
(2)(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549ef2a5b6592308c2da9233aca63e77.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6429dd74013b8984de8dcaac9c862957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52121b304f70afcb2dfb3d4a614f7224.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d177a7489e327bff83e61ac1eeaaf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac5235bf88c507cd6178e94914133d04.png)
您最近一年使用:0次
名校
解题方法
2 . 已知点
是抛物线
上不同三点,直线
与抛物线
相切.
(1)若直线
的斜率为2,线段
的中点为
,求
的方程;
(2)若
为定值,当
变动时,判断
是否为定值,若为定值,求出该定值;若不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35644a7d25d0410409238f52c8818083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e39bd21af422662049290a3aa4841b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dec2ca6438c82b43f746057d8129885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e325d1e4485ec4cfb3d7bb038d675d7d.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18fe48905f1e58b2fe08706c2f53b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13d726b14a313e000a81526162f35748.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b3c5a4887dfe02b02ee90d740151e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1835c6f51b4471243b5e1a3d6e74c203.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)当
时,求函数
的单调区间和极值;
(2)当
时,不等式
恒成立,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9051c82f5a34a4635202f3fe72e32fdc.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ce6227807fd76d382863bff2f89ef80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-03-21更新
|
1238次组卷
|
4卷引用:江西省吉安市第一中学2024届高三三模数学试题
名校
解题方法
4 . 已知数列
的前
项和为
,满足
;数列
满足
,其中
.
(1)求数列
的通项公式;
(2)对于给定的正整数
,在
和
之间插入
个数
,使
,
成等差数列.
(i)求
;
(ii)是否存在正整数
,使得
恰好是数列
或
中的项?若存在,求出所有满足条件的
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.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/83fd67e206753eff52406291c19daa38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23f7f601ad9971d3de3e2dd820642e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59dd6c97d2ee3e74ba5730f1cbcc1d43.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0197eeeeaafec6b1fdd7bb8509572f6b.png)
(2)对于给定的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd6f136f7c8d27b406c0993dcfece54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50a272adba0f1120109824440f0e252c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b8d5b6045219ea4527202ab131bb2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417083c7157cf0b45befc7c537f1012c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/629e172f62f389ea84b7d771c1c27566.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a039f1df440117fe89030a4ad6dcf291.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22be6bbf70b5c135edaf8db69118cb50.png)
(ii)是否存在正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d75ed0812322ed46d25ec41f609674be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-03-19更新
|
2008次组卷
|
6卷引用:江西省吉安市第一中学2024届高三下学期期中考试数学试题
名校
5 . 已知点
,集合
,点
,且对于S中任何异于P的点Q,都有
.
(1)试判断点P关于椭圆
的位置关系,并说明理由;
(2)求P的坐标;
(3)设椭圆
的焦点为
,
,证明:
.
[参考公式:
]
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaa5580264df7f4de9c4c5fc58b18f74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a06a3be9d9e57cc8b751d96554505a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59a135407ec0cda6aa39c90fe7035ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a48e5e0a68100438208403a9713edfd.png)
(1)试判断点P关于椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914075a4574c09bdb860d8f8f09a4e7a.png)
(2)求P的坐标;
(3)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914075a4574c09bdb860d8f8f09a4e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8cdfb95ccff9cfdc84267f06f2033c8.png)
[参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22af82504f580fec0fc5be95df627671.png)
您最近一年使用:0次
2024-02-03更新
|
375次组卷
|
2卷引用:江西省吉安市峡江中学2023-2024学年高二上学期期末数学试卷(九省联考题型)
6 . 高斯是德国著名数学家,近代数学的奠基者之一,享有“数学王子”的称号,用他名字定义的函数
称为高斯函数,其中
表示不超过x的最大整数,如
,
,已知数列
满足
,
,
,若
,
为数列
的前n项和,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1550a97c21c1d71c9e95dde569668be0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d54a0e82778f606d95a486835ac9f56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f2323cbdf0b1b71092c962ae705102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1928c254cfada1f75a5cd1e34db5a63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d845281cd834068104af1b1aa6027c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7231e303ae39572f6c359c5e83822075.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5735a391a46cfdbd63e171769f8abb38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25c3ac959bdf1b78cb98d92b87c91c46.png)
A.2026 | B.2025 | C.2024 | D.2023 |
您最近一年使用:0次
2023-11-25更新
|
930次组卷
|
7卷引用:江西省吉安市双校联盟2022-2023学年高二下学期期中考试数学试题
江西省吉安市双校联盟2022-2023学年高二下学期期中考试数学试题云南省曲靖市第一中学2022-2023学年高一下学期7月期末考试数学试题内蒙古赤峰市赤峰二中2024届高三上学期第三次月考数学(理)试题(已下线)第五章 数列 专题8 数列中的递推(已下线)第五章 数列 专题7 有关数列求通项、周期性求和的问题陕西省西安市西安中学2024届高三上学期期末数学(理)试题(已下线)4.3.2 等比数列的前n项和公式——课后作业(巩固版)
名校
解题方法
7 . 已知函数
.
(1)若
,求
的单调区间与极值;
(2)若当
时,恒有
,求
的取值范围;
(3)设
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c2c109a0eeb9b5ce9638ce870f2733b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e02125e0a1f3cda39742b765baa74c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a70b95c53fb6655721e2a8c61f5c2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f822d91591438e66e060d813e61aae4.png)
您最近一年使用:0次
2023-11-19更新
|
385次组卷
|
3卷引用:江西省吉安市吉州区吉安一中2023-2024学年高三上学期期中数学试题
江西省吉安市吉州区吉安一中2023-2024学年高三上学期期中数学试题(已下线)模块六 全真模拟篇 拔高2 期末终极研习室(2023-2024学年第一学期)高三山东省青岛市第十七中学2024届高三上学期期末检测数学试题
8 . 已知函数
,其中
,
(1)若
,
(i)当
时,求
的单调区间;
(ii)曲线
与直线
有且仅有两个交点,求
的取值范围.
(2)证明:当
时,存在直线
,使直线
是曲线
的切线,也是曲线
的切线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3373d211a4a1bf81e1ebfb146fcddf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3a42b6fd4fff031515c4845db4a947.png)
(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
(ii)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50866229ec5a3640fb250f9bd2192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932e474e861cbef4611e8bdebf2814f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
您最近一年使用:0次
2023-04-26更新
|
997次组卷
|
2卷引用:江西省万安中学2024届高三上学期开学考试数学试题
名校
解题方法
9 . 已知
,函数
,
.
(1)若
,求证:
在
上是增函数;
(2)若存在
,使得
对于任意的
成立,求最大的整数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fe84ecdcafb66c2e3a4dd702503729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9f049a5f960728c60a909821b2404b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d64a995531a220eee02c2ce7eedf72c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
(2)若存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0168f9b0c3d089f6a5984587c8d216a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2023-03-26更新
|
679次组卷
|
4卷引用:江西省万安中学2022-2023学年高二下学期期中数学试题
江西省万安中学2022-2023学年高二下学期期中数学试题四川省宜宾市2023届高三下学期第二次诊断性测试理科数学试题(已下线)专题20利用导数研究不等问题(已下线)重难点突破10 利用导数解决一类整数问题(四大题型)
解题方法
10 . 双曲线C:
的离心率为
,圆O:
与x轴正半轴交于点A,圆O在点A处的切线被双曲线C截得的弦长为
.
(1)求双曲线C的方程;
(2)设圆O上任意一点P处的切线交双曲线C于两点M、N,试判断
是否为定值?若为定值,求出该定值;若不是定值,请说明理由;
(3)若将(2)中的双曲线改为椭圆
,其他条件不变,试探讨
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求双曲线C的方程;
(2)设圆O上任意一点P处的切线交双曲线C于两点M、N,试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79188647c574441c2414c3781a0ef543.png)
(3)若将(2)中的双曲线改为椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c03c6b8d7418edf20f474389971352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79188647c574441c2414c3781a0ef543.png)
您最近一年使用:0次