解题方法
1 . 定义在
上的奇函数
满足
,当
时,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62786326087b00d188862aa70b0a8ef8.png)
______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b568b2cee9ef2a32d2f27305a9104d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab87accf1942ab80def96d12ef173163.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2e2462668b89dd526729fe032e0600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62786326087b00d188862aa70b0a8ef8.png)
您最近一年使用:0次
名校
解题方法
2 . 在
中,M是边BC的中点,N是线段BM的中点.设
,
,记
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf5c1d124e8e023fe8e8c5ef3412813.png)
__________ ;若
,
的面积为
,则当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a779e711b3900db89bd868360dcfaa.png)
__________ 时,
取得最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b9d8a08fc52c31cc1a7f527d18b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f386f5b56b07b96f2600da1be15414a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc51bdc8c2c18379db1affbb06f8923f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf5c1d124e8e023fe8e8c5ef3412813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c06393c604df2200ce9fd4bc9e67c2ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a779e711b3900db89bd868360dcfaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e6f0e94393fc6bbd9b4b83ede534ac.png)
您最近一年使用:0次
2024-03-01更新
|
1447次组卷
|
6卷引用:天津市和平区耀华中学2024届高三下学期寒假验收考数学试卷
天津市和平区耀华中学2024届高三下学期寒假验收考数学试卷天津市实验中学滨海学校2023-2024学年高一下学期随堂质量监测(月考)数学试题(已下线)信息必刷卷04(天津专用)(已下线)2024年天津高考数学真题平行卷(提升)(已下线)第2套 新高考新结构全真模拟2(艺体生)(已下线)压轴题03不等式压轴题13题型汇总 -1
3 . 若函数
(
,
)的最小正周期为
,且
.给出下列判断:
①若
,则函数
的图象关于直线
对称
②若
在区间
上单调递增,则
的取值范围是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2e40d1e4d047249453f36ce4e60377.png)
③若
在区间
内没有零点,则
的取值范围是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b3189ba678499e528de7574e5adbf33.png)
④若
的图象与直线
在
上有且仅有1个交点,则
的取值范围是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a35af404cb8618c09a8040fff9fb1e9c.png)
其中,判断正确的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306bc38c05e863481825f5639cea9ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7c9e46448bc791c441ca02d8f4508eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb6e52d1733c6ce9f78ba2bfe142355.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c404ebac6d321a29190c57b1c9c55ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c63e1c64c42b7f3b7fdc396d4756cab.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/620709ed747abad41e3a58a0c64dd875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2e40d1e4d047249453f36ce4e60377.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc9bbf6e7847f96706b54f079716bf23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b3189ba678499e528de7574e5adbf33.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefa44964db83759aff6fc8dd7ef8f28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bccd6a6e85bdf500218a3e75b31f3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074c228ffc7b1e306f8410afe7bc4b5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a35af404cb8618c09a8040fff9fb1e9c.png)
其中,判断正确的个数为( )
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2024-01-18更新
|
871次组卷
|
2卷引用:天津市和平区耀华中学2024届高三下学期寒假验收考数学试卷
4 . 已知椭圆
的左顶点为点A,上、下顶点分别为点B、C,左焦点为点F,且椭圆的焦距为
,
为等边三角形.
(1)求椭圆的方程及离心率;
(2)设过原点O且斜率为
的直线l与椭圆交于P、Q两点,直线l与直线AB交于点M,且点P、M均在第一象限.若
的面积是
的面积的2倍,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
(1)求椭圆的方程及离心率;
(2)设过原点O且斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6bdac20e214b2cb3bd07f8d4778dcca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8dcc9f79fe5f07f25447aa442ee14ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b886208c6c2df19b984f2631e1c996.png)
您最近一年使用:0次
2024-01-16更新
|
512次组卷
|
2卷引用:天津市第一中学滨海学校2024届高三第六次学业水平质量调查数学试卷(开学考)
名校
5 . 黎曼猜想是解析数论里的一个重要猜想,它被很多数学家视为是最重要的数学猜想之一.它与函数
(
,s为常数)密切相关,请解决下列问题.
(1)当
时,讨论
的单调性;
(2)当
时;
①证明
有唯一极值点;
②记
的唯一极值点为
,讨论
的单调性,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755d78f27a96bf14b96dff9913851df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b862659eee15ac003d2d2c53d9abbf5c.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b366d99460274e9ab2187c11af8a6372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f15bcd4917a74ec6f505f0e10833a7f.png)
①证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
②记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010dec4fc2df0b58992eb4515cd13eff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010dec4fc2df0b58992eb4515cd13eff.png)
您最近一年使用:0次
2024-01-15更新
|
2868次组卷
|
9卷引用:天津市第一中学滨海学校2024届高三第六次学业水平质量调查数学试卷(开学考)
天津市第一中学滨海学校2024届高三第六次学业水平质量调查数学试卷(开学考)2024届广东省惠州市大亚湾区普通高中毕业年级联合模拟考试(一)数学试卷2024届广东省大湾区普通高中毕业年级联合模拟考试(一)数学试题湖南省长沙市长郡中学2024届高三一模数学试题(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编吉林省通化市梅河口市第五中学2024届高三下学期一模数学试题(已下线)专题2 导数与函数的极值、最值【练】辽宁省锦州市某校2023-2024学年高三下学期考前测试数学试卷(A)河南省信阳市新县高级中学2024届高三考前第七次适应性考试数学试题
名校
解题方法
6 . 任取一个正整数,若是奇数,就将该数乘3再加上1;若是偶数,就将该数除以2.反复进行上述两种运算,经过有限次步骤后,必进入循环圈
.这就是数学史上著名的“冰雹猜想”(又称“角谷猜想”).如取正整数
,根据上述运算法则得出
,共需经过8个步骤变成1(简称为8步“雹程”).现给出冰雹猜想的递推关系如下:已知数列
满足:
(
为正整数),
当
时,
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a16f78ce0dab1ac8fa6abbd70f2b008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3967d620e2fef3ecc724c66e29f68a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a73700b5135fc6a9c2d923a27a4c9b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/999ac8c1ef39251e07a7fc54cbf7e26e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4914df4e75585d5ff7709d64a23611.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8a3cc8c48bf54ec8252e5dce6867754.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59097ad7c8f3fcff871ad48933d30498.png)
A.170 | B.168 | C.130 | D.172 |
您最近一年使用:0次
2024-01-12更新
|
920次组卷
|
4卷引用:天津市和平区耀华中学2024届高三下学期寒假验收考数学试卷
名校
解题方法
7 . 已知椭圆C:
的离心率为
长轴的右端点为
.
(1)求C的方程;
(2)不经过点A的直线
与椭圆C分别相交于
两点,且以MN为直径的圆过点
,
①试证明直线
过一定点,并求出此定点;
②从点
作
垂足为
,点
写出
的最小值(结论不要求证明).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58a0b452fd57bbdc105589e871baa009.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ba447f2abb9bd37cc8d3f607f7e694a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de255124598a717187ee85cb944be05.png)
(1)求C的方程;
(2)不经过点A的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
①试证明直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
②从点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7920d2550a6af7df3db60a33fe02c53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68967218fdc94c817f0e3b380cce22c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e60436c1f7b5c2f6b5331548216e8077.png)
您最近一年使用:0次
名校
8 . 已知函数
,
.
(1)讨论
的单调性;
(2)当
时,若
的极小值点为
,证明:
存在唯一的零点
,且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b62446c55270cc760f268c60de71a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3002ad1638f25e355d70d5ab63e637f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1d9ff5befe43e47d35e5662859f0f18.png)
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2024-01-02更新
|
1055次组卷
|
4卷引用:高三数学开学摸底考(天津专用)
(已下线)高三数学开学摸底考(天津专用)广东省深圳实验、湛江一中、珠海一中三校2024届高三上学期12月联考数学试题江苏省苏州市相城区南京师大苏州实验学校2024届高三上学期期末模拟数学试题(已下线)模块三 大招11 隐零点代换
名校
解题方法
9 . 已知函数
,
.
(1)若函数
在
处的切线与直线
垂直,求实数k的值;
(2)设
,当
时,
(i)证明:函数
存在唯一的极大值点
;
(ii)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/974e5136a812bf23d7390093aa6db141.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726c78f7ddc45407509df9f4d3dc6b3f.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e8f77e3876694978a22975eff397375.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb48434bdcafb5e084fc0b6396cb9469.png)
(i)证明:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb482aa5e8d535919785d3e3e1f2d7f6.png)
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名校
解题方法
10 . 已知等比数列
是递增数列,且
,
.
(1)求
通项公式;
(2)在
和
之间插入1个数
,使
、
、
成等差数列;在
和
之间插入2个数
、
,使
、
、
、
成等差数列;…;在
和
之间插入
个数
、
、…、
,使
、
、
、…、
、
成等差数列.若
,且
对
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ef35b21da4cd8130642539d8245f83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964df3e9308711d7e14fb624b0c25e2f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e84bbc85887baf2c01afa80b0d5cc24b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e84bbc85887baf2c01afa80b0d5cc24b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a558b61154c775d249113804c1453f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50c4bd1eb1fa1f4fdc8392b59e6b6f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a558b61154c775d249113804c1453f2.png)
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