名校
解题方法
1 . 已知
,
.
(1)求
在
上的最小值;
(2)求曲线
在
处的切线方程
,并证明:
,都有
;
(3)若方程
有两个不相等的实数根
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9b6a91900d0dfa6296cdee22fdd6fe6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea17ec8f211e8be2571fbcce23e04eb8.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23a03ca8f1729bfcadf513784817fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3add1679c27392a1a7f635723a4b36eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa18838a13fda4e45612c32cdf98b71.png)
(3)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338316b0fe50fdea0f2f75aec4c990dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd888afdcfdb3e91a157d50f65e915e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8013645996eb5766aaf7de48d243d1de.png)
您最近一年使用:0次
名校
解题方法
2 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4426c3b6aa8912905c67d9a26d07083a.png)
(1)若
恒成立,求
的值;
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4426c3b6aa8912905c67d9a26d07083a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226648ae7c1bc686358268a0cdc12ef4.png)
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3 . 设p为任意给定的大于1的整数,每个正整数n均可以唯一地表示成
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9065ce45fd23edbaf85a45ff15c2fc6d.png)
,我们将
称为n的p进制表示,将
称为n在p进制下的数字和.例如:由
可知
,
.
(1)请给出2024的三进制表示;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3f3539f44a967ded37d695b8c5a754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9065ce45fd23edbaf85a45ff15c2fc6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebb7c6bb11637246e20a186de268f0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d451ea758732eb3e8530a0e510efd835.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce766f5a782ee1123eaaf4ec9773f3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa82a1ee441389e563ed32c2c660b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cf0d4f1ae3c405709ffc9215063ee21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d10a86dea76b9b21e2c221fab3a6a167.png)
(1)请给出2024的三进制表示;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8f8cbdf6bfa897019ce1eb963a869f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32c363c1fc5f6c82234385e8e96fb644.png)
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名校
4 . 函数
的图象关于坐标原点成中心对称图形的充要条件是函数
为奇函数,有同学发现可以将其推广为:函数
的图象关于点
成中心对称图形的充要条件是函数
为奇函数.已知函数
.
(1)若函数
的对称中心为
,求函数
的解析式.
(2)由代数基本定理可以得到:任何一元
次复系数多项式
在复数集中可以分解为n个一次因式的乘积.进而,一元n次多项式方程有n个复数根(重根按重数计).如设实系数一元二次方程
,在复数集内的根为
,
,则方程
可变形为
,展开得:
则有
,即
,类比上述推理方法可得实系数一元三次方程根与系数的关系.
①若
,方程
在复数集内的根为
,当
时,求
的最大值;
②若
,函数
的零点分别为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/684eae051519f6aba934423a7182fa0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018e805194ffdc598b05f066b3ea6ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3279d65343e1b0bcdf8aed2d8522df0d.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257dd4ddacb8667a761be897568f3674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
(2)由代数基本定理可以得到:任何一元
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd7cf9e14c5762b28e2b626ee5a7c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ad4bce39424043f2693a5f49f48d85e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7096476deb4b0b86a15c66856b93ba79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c9080eed5461a719145aa1e768c6ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad2afb260459e1708cd3b619f1f5a0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a15e691d7c439329b7c74ae0bc678ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8824ecc19d6daa94cb22ea94716296d6.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb291880ef86317d079c0e0b349403e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0150d1fd43abcd4894550d40c5ac9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5bc4081a1bbf3e7b0a1c856975a0b9e.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a87f1b2ac4c09de232650533da16a300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b00232b29c9fe2cc1b3f8bcb4dcaad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73c1d26e119ff006209f50b5326fc3bb.png)
您最近一年使用:0次
名校
5 . 设定义在R上的可导函数
和
满足
,
,
为奇函数,且
. 则下列选项中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a024eb03d7ffb3b510d1a131af3576bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8234c7ea70bdc98b92dee03cd5cb67a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc2b7be871fef904c94ef6360ee32bb.png)
A.![]() |
B.![]() |
C.![]() ![]() |
D.![]() |
您最近一年使用:0次
2024-02-04更新
|
1410次组卷
|
6卷引用:安徽省芜湖市安徽师大附中2023-2024学年高二下学期3月测试数学试题
6 . 已知圆C过点
,
,
.
(1)求圆C的标准方程;
(2)若过点C且与x轴平行的直线与圆C交于点M,N,点P为直线
上的动点,直线PM,PN与圆C的另一个交点分别为E,F(EF与MN不重合),证明:直线EF过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbc43e72034cfce8e9d75b55c537287c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7ffc33191f71a87fc60694a54227ac.png)
(1)求圆C的标准方程;
(2)若过点C且与x轴平行的直线与圆C交于点M,N,点P为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da322ac8867e8a47c6588601078abf18.png)
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7 . 已知函数
,
,
有两个零点
,
.
(1)若
,求
的最小值;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23d03f36d61139bad5c18f55d978112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b586fb1043595a3dc45e21e3497dea13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/587ff1ef10c9c8ba55de8cfa7711c70a.png)
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解题方法
8 . 已知正项数列
满足:
,
,则以下结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/798b81ff16b427407e6a47ba4e452498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
9 . 已知点
,动点
到直线
的距离为
,且
,记
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过
作圆
的两条切线分别交曲线
于A,B两点,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce176fdfbb44b8459f441a8d805013f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ff7e0ef1f622120cc1b18e9d3e80ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f11c89c6066ef6d969cb33d0a76ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d6812ef0f8739267591414173891e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe659fb4ca96554eeefd6a305ea1a70d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a11cb104b04c4e6a1be700e81da279a.png)
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10 . 设
是坐标平面
上的一点,曲线
是函数
的图象.若过点
恰能作曲线
的
条切线
,则称
是函数
的“
度点”.
(1)判断点
与点
是否为函数
的1度点,不需要说明理由;
(2)已知
,
.证明:点
是
的0度点;
(3)求函数
的全体2度点构成的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0963e06ca1a0aa7899759b13bab7db21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)判断点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2071086f9c57d5b02520606c56cf372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976581d4a974fe50f9f29d430c1289f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c955376eaa10efc765563bf426634df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e43dac42d94c14cdb71b4f9a6e97a7e.png)
(3)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0660d4864c16652a6b27337462b3f1.png)
您最近一年使用:0次
2024-01-13更新
|
1187次组卷
|
10卷引用:安徽省安庆市第一中学2022-2023学年高二下学期第二次段考数学试题
安徽省安庆市第一中学2022-2023学年高二下学期第二次段考数学试题上海市松江一中2022-2023学年高二下学期5月月考数学试题上海市浦东新区2023届高三二模数学试题(已下线)专题02 函数及其应用(已下线)重难点04导数的应用六种解法(1)(已下线)专题19 导数综合-2江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(六)江苏省姜堰中学2024届高三下学期阶段性测试(2.5模)数学试题(已下线)压轴题01集合新定义、函数与导数13题型汇总-2上海市向明中学2024届高三下学期三模测试数学试卷