名校
解题方法
1 . 已知椭圆
:
(
)的左、右焦点分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
,点P是
上一点,直线l:
(
).
(1)当
时,已知直线l恰经过
的右顶点A,求m的值;
(2)当
时,若P同时是l上一点且
,求a的值;
(3)设直线
交l于点Q,对每一个给定的
,任意满足
的实数a,都有
成立.则当m变化时,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f9b6b54e434819f50ae1349f534abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b7fcfde0f8949461eb9ea7af43ede8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff99ce2491f3b979cbbfbc5e9f8d9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d670dcd0ce51abe372bc51a88ba1a7.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af039cad52ca4e1f1e322277bc81afd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a71a658362bd9faa329c3d9f6e6d2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377923225cb490323c85e4e5a12643e5.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d670dcd0ce51abe372bc51a88ba1a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697cf7097b0133b2598b697fa8470d9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee83676fa76e3f845ab3d47ad678a8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b213e4e1164ff957df10996756912a7c.png)
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2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28e4867492d6035296db5e28c6ed599.png)
(1)当
时,求
的零点;
(2)若
恰有两个极值点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f28e4867492d6035296db5e28c6ed599.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-06-18更新
|
489次组卷
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5卷引用:重庆市第四十九中学校、江津第二中学校等九校2023-2024学年高二下学期5月联考数学试题
名校
解题方法
3 . (1)已知函数
,证明:
,
,
.
(2)已知函数
,定义:若存在
,
,使得曲线
在点
与点
处有相同的切线
,则称切线
为“自公切线”.
①证明:当
时,曲线
不存在“自公切线”;
②讨论曲线
的“自公切线”的条数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff6838d84b68c6f0d3b93b196d9b08d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673207f6b77b8192d25463d071737b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bf60c5e8996d138198fe74f30ce520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da092efa74406128332df5a053685a8.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aba730d4e2ff4c9cc155446b3d12e96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a93969738a9bb969f40cf587f1d5d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878fd4af5b8fff01627f560767e19b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4197070db34f0419b6d85eed4cec9fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
①证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
②讨论曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
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4 . 若关于x的不等式
恒成立,则实数a的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc1d431cbbb931fabf803a49148f73d.png)
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2024-06-17更新
|
141次组卷
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2卷引用:山西省部分学校2023-2024学年高二下学期5月质量检测数学试题
名校
解题方法
5 . 已知函数
,
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b647867d91de52884cea8c492fb0f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b29e5cc1e369f351eb1b505919f6ab.png)
A.函数![]() ![]() ![]() |
B.令![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() |
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2024-06-16更新
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名校
6 . 函数
是我们最熟悉的函数之一,它是奇函数,且y轴和直线
是它的渐近线,在第一象限和第三象限存在图象,其图象实质是圆锥曲线中的双曲线.
的图象不仅是中心对称图形,而且还是轴对称图形,求其对称轴l的方程;
(2)若保持原点不动,长度单位不变,只改变坐标轴的方向的坐标系的变换,叫坐标系的旋转,简称转轴.
(i)请采用适当的变换方法,求函数
变换后所对应的双曲线标准方程;
(ii)已知函数
图象上任一点到平面内定点
的距离差的绝对值为定值,以线段
为直径的圆与
的图象一个交点为
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
(2)若保持原点不动,长度单位不变,只改变坐标轴的方向的坐标系的变换,叫坐标系的旋转,简称转轴.
(i)请采用适当的变换方法,求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
(ii)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1305b9abebd7bef3171486df157286b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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2024-06-15更新
|
91次组卷
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2卷引用:山西省晋城市第一中学校2023-2024学年高二下学期第四次调研考试(5月)数学试题
解题方法
7 . 已知数列
是斐波那契数列,其数值为:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4fb1a2d1cb1152ef78d7332d45b681.png)
.这一数列以如下递推的方法定义:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642c7410a3134bed37df637e8d382c88.png)
.数列
对于确定的正整数
,若存在正整数
使得
成立,则称数列
为“
阶可分拆数列”.
(1)已知数列
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c9e8b08ba803f851cf12404e742775.png)
.判断是否对
,总存在确定的正整数
,使得数列
为“
阶可分拆数列”,并说明理由.
(2)设数列
的前
项和为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75541174a021adfd2e3356ca2ad56f7b.png)
,
(i)若数列
为“
阶可分拆数列”,求出符合条件的实数
的值;
(ii)在(i)问的前提下,若数列
满足
,
,其前
项和为
.证明:当
且
时,
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a4fb1a2d1cb1152ef78d7332d45b681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc50612eece655796b752da6b4bc3f3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642c7410a3134bed37df637e8d382c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d74fa7fa6330976d7eb8e523a62cd09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cdfd9c3f8933cddb63d87dbe2812994.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f329b217e1051b23f0d61023cdc6e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c9e8b08ba803f851cf12404e742775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/753358ca020523f27725f5187bb8e988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/136a003907c455bfd58875c96c138772.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ab0309e2cd35585ea9fb2cc3017abf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75541174a021adfd2e3356ca2ad56f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79282bbe9f6408297d6378878c423bec.png)
(i)若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d813f3ca8db41a4db6c18eac30fef98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(ii)在(i)问的前提下,若数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5f894d605847c6df0c4df24cf8e1fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69a340cb0e3c456ec64ffdf89d7cd6ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09881de0dc186bbcd1e60eb00159ee97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48268fd6d3f92032eb54fbf65c01405.png)
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8 . 已知
.
(1)求
的单调区间及极值;
(2)(i)
恒成立,求a的取值范围;
(ii)证明
时,
;
(3)
时,
恒成立,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8830a1a93d3958583f63c4c89f73223a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(2)(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dc9ede2e55724383dd1093fc7fcdb59.png)
(ii)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c865fc7e9f9538b1391a6adbadb111bd.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b4955c5adc717b7f6f0b975e0724ff5.png)
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解题方法
9 . 函数
有三个不同极值点
,且
.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf42654d900f4ca45ba473d9ba363b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7af029ff25c826608dc72348532407.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-06-14更新
|
104次组卷
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2卷引用:山西省晋城市第一中学校2023-2024学年高二下学期第四次调研考试(5月)数学试题
名校
解题方法
10 . 已知偶函数
与其导函数
定义域均为
,
为奇函数,若2是
的极值点,则
在区间
内解的个数最少有( )个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4a364dbaef735e2530b11d95b0e9c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f168b6811f1da5f09db1d9984ad8664f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1daa67de3b8971d54ced0cac0cd11f2e.png)
A.7 | B.8 | C.9 | D.11 |
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2024-06-14更新
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119次组卷
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2卷引用:山西省晋城市第一中学校2023-2024学年高二下学期第四次调研考试(5月)数学试题