解题方法
1 . 已知
,
,P点满足
.
(1)求点P的轨迹
的方程,并说明是何图形;
(2)设T为直线
上一点,直线TO,TA分别与
相交于点B,C,求四边形
面积S的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/109a293cef44f23e86e22c1a4cfcbbe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f153ab48e0dae18f11335b117bf955.png)
(1)求点P的轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)设T为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5241e0e07a9cd48e4f853405dca1a03.png)
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名校
2 . 定义函数
.
(1)求曲线
在
处的切线斜率;
(2)若
对任意
恒成立,求k的取值范围;
(3)讨论函数
的零点个数,并判断
是否有最小值.若
有最小值m﹐证明:
;若
没有最小值,说明理由.
(注:
…是自然对数的底数)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499fb4d972a3f0fe389b533aa342dc72.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84153925db492238052d0baf65ae0abc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82cecbba960d24990f19054c9ec35d79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(3)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66fd6dda73649dcd9df1ed271b77ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89220eb96a4757f2988362bc04e80c9.png)
(注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9405dfcca25b76af059fb4c308983eae.png)
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2023-12-19更新
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1049次组卷
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5卷引用:山东省名校考试联盟2024届高三上学期12月阶段性检测数学试题
山东省名校考试联盟2024届高三上学期12月阶段性检测数学试题江苏省扬州市扬州中学2024届高三上学期1月阶段性检测数学试题江苏省镇江市丹阳高级中学2024届高三下学期2月阶段检测数学试题(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(已下线)专题22 新高考新题型第19题新定义压轴解答题归纳(9大核心考点)(讲义)
3 . 若函数
在定义域
上满足
,且
时
,定义域为
的
为偶函数.
(1)求证:函数
在定义域上单调递增.
(2)若在区间
上,
;
在
上的图象关于点
对称.
(i)求函数
和函数
在区间
上的解析式.
(ii)若关于x的不等式
,
对任意定义域内的
恒成立,求实数
存在时,
的最大值关于a的函数关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dea20bf4103d4a86ce2dedc8cbf73498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d991a665834f1957063731202084570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若在区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c01b3dea6d0449097da0edc9130ef2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b577bf976fc3acd92b4af89be960359f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e110165a664ac7a77e70a6a46078602b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a948d2f7732d7f03e986c63712089b.png)
(i)求函数
![](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/7d991a665834f1957063731202084570.png)
(ii)若关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2846c1cedbe564d20873d2b4d6f426aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6232dc74b15e4acb0ac3482a1cbe6a52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157416e0bb98baff8059b9ef0e123ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2023-12-14更新
|
940次组卷
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6卷引用:山东省德州市万隆中英文高级中学2023-2024学年高二下学期6月月考数学试题
山东省德州市万隆中英文高级中学2023-2024学年高二下学期6月月考数学试题辽宁省大连市2022-2023学年高一上学期期末数学模拟试题(已下线)高一上学期期末考试解答题压轴题50题专练-举一反三系列福建省福州市九师教学联盟2023-2024学年高一上学期1月联考数学试题江西省上饶市广丰区丰溪中学2023-2024学年高一上学期期末模拟数学试题(已下线)高一数学开学摸底考 01-人教A版2019必修第一册全册开学摸底考试卷
名校
解题方法
4 . 山东省青岛第二中学始建于1925年,悠悠历史翻开新篇:2025年,青岛二中将迎来百年校庆.在2023年11月8日立冬这天,二中学子摩拳擦掌,开始阶段性考试.若
是定义在
上的奇函数,对于任意给定的不等正实数
,不等式
恒成立,且
,设
为“立冬函数”,则满足“立冬函数”
的x的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a271c3a5d9880c1b15b581dac2c166a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f003178e540e09aebb952c33a3a685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c45b699cedb3c1868e77f224603227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc0879734ee766cb630cfeb3f25fea7d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知
,函数
有两个极值点
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/592b5bcafcca41fb04a5364c928a721a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
A.a可能是负数 |
B.若![]() ![]() ![]() ![]() |
C.![]() |
D.若存在![]() ![]() ![]() |
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2卷引用:山东省临沂市罗庄区2024届高三上学期学科素养水平监测数学试题
解题方法
6 . 已知四棱锥
中,底面
是边长为2的正方形,
平面
,
,且以
为圆心、
为半径的圆分别交
,
于
,
两点,点
是劣弧
上的动点,其中
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e124a392dc84fcc1662fe6d896aa12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c9ac405301d3c27523ee19ba415315.png)
A.弧![]() ![]() ![]() ![]() ![]() |
B.弧![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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2023-11-28更新
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2卷引用:山东省潍坊市部分市区2023-2024学年高二上学期期中质量监测数学试题
名校
解题方法
7 . 已知函数
的图象可由函数
(
且
)的图象先向下平移2个单位长度,再向左平移1个单位长度得到,且
.
(1)求
的值;
(2)若函数
,证明:
;
(3)若函数
与
在区间
上都是单调的,且单调性相同,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42e6f7234a6a37987de4cdce6f026331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93acdd1905e7b9374f0644820fb3fd71.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8f4b6dabbadf37d201eadf7486dc98c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abea70e7e8122478683bc072aa38095.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b9a99afeadaec62a56019ff61e04c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/496fd07ac35a34a6d0edfead2aeef41a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6c1756b564bf1d998d8179637011c88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-11-23更新
|
343次组卷
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2卷引用:山东省菏泽市第一中学2023-2024学年高一上学期12月月考数学试题
名校
解题方法
8 . 如图,扇形
是某社区的一块空地平面图,点
在弧
上(异于
两点),
,垂足分别为
,
米.该社区物业公司计划将四边形
区域作为儿童娱乐设施建筑用地,其余的地方种植花卉,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5f7a76c82ae9db81b4ade441de1b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3f92b0d5b0dffdd4db704a716befee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/510e7545c07cfc7c976a538c81f957ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/033274547930b2e2dcd4ea4919a36738.png)
A.当![]() ![]() |
B.当![]() ![]() |
C.儿童娱乐设施建筑用地面积的最大值为![]() |
D.种植花卉区域的面积可能是![]() |
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2023-11-21更新
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713次组卷
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3卷引用:山东省青岛市即墨区第一中学2023-2024学年高一下学期第一次阶段检测数学试题
山东省青岛市即墨区第一中学2023-2024学年高一下学期第一次阶段检测数学试题山西省2023-2024学年高三11月联合考试模拟预测数学试题(已下线)压轴题07三角函数与正余弦定理压轴题9题型汇总-2
名校
解题方法
9 . 如图所示,正方体
的棱长为3,动点
在底面正方形
内,且
与两个定点
,
的距离之比为
.
的轨迹方程,并说明轨迹的形状;
(2)求动点
到平面
的距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95628327dc58037e5368f4404c05ec39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8406f2441769ce49264ccca6585dc9.png)
您最近一年使用:0次
名校
10 . 已知正四棱柱
的底面边长为
,点
分别满足
.甲、乙、丙、丁四名同学利用《空间向量与立体几何》这一章的知识对其进行研究,各自得出一个结论:
甲:当
时,存在
,使得
;
乙:当
时,存在
,
,使得
;
丙:当
时,满足
的
的关系为
;
丁:当
时,满足
的点
围成区域的面积为
.
其中得出错误结论的同学有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4586c36ecaff9aa606b6148eb28484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8866c9f57fab68f4d3aa0cd809e31cc.png)
甲:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8493a0cd10d3d0399173c04163740a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec6fb9e0625b85be3103d317fbb0cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff480d049f3f174b970cedd14aa4d4c.png)
乙:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8493a0cd10d3d0399173c04163740a38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f199f086ffa007bd2d64db066890ca2b.png)
丙:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4325a91861fa8269194667d6288e7e63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc43c738e927f9c0038cc1bf86d019b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec6fb9e0625b85be3103d317fbb0cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbae94f2dd5086f7ddbe18407a978e9b.png)
丁:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc620ca3717dda78975de0a1568587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff480d049f3f174b970cedd14aa4d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
其中得出错误结论的同学有( )
A.甲 | B.乙 | C.丙 | D.丁 |
您最近一年使用:0次
2023-11-15更新
|
368次组卷
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