解题方法
1 . 已知函数
.
(1)若
恒成立,求实数
的取值范围;
(2)设
满足
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2708a1682ea700eacab1dd03e1fc4b1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e38c541dec8fce1d26886e5ef7d21f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7abcc774655c0561987ba6e657160d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2037b0bad7c7a312bac1ac0653d9a491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca13a93b5f401c0d39ba52b0cffcb0.png)
您最近一年使用:0次
2024-05-20更新
|
532次组卷
|
2卷引用:山西省太原市2023-2024学年高二下学期4月期中学业诊断数学试题
名校
解题方法
2 . 已知椭圆C:
过点
,且它的长轴长是短轴长的3倍.斜率为
的直线l与椭圆C交于A,B两点(如图所示,点P在直线l的上方).
(2)试判断直线PA,PB的斜率和是否为定值?若是,求出这个定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b68f42934c74e0d759a67613a1da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e54170c4708bd5e9f4b4d8db0aa91e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
(2)试判断直线PA,PB的斜率和是否为定值?若是,求出这个定值;若不是,请说明理由.
您最近一年使用:0次
2024-03-29更新
|
167次组卷
|
2卷引用:山西省太原市尖草坪区第一中学校2023-2024学年高二下学期3月质量监测数学试题
名校
解题方法
3 .
元向量(
)也叫
维向量,是平面向量的推广,设
为正整数,数集
中的
个元素构成的有序组
称为
上的
元向量,其中
为该向量的第
个分量.
元向量通常用希腊字母
等表示,如
上全体
元向量构成的集合记为
.对于
,记
,定义如下运算:加法法则
,模公式
,内积
,设
的夹角为
,则
.
(1)设
,解决下面问题:
①求
;
②设
与
的夹角为
,求
;
(2)对于一个
元向量
,若
,称
为
维信号向量.规定
,已知
个两两垂直的120维信号向量
满足它们的前
个分量都相同,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d617b088816e03a283123e29e4dbdca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/086eb439f6a1578fdba904825340772d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efee470d0232b6b37f2fb2ab15aae0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/948eea3409b959c7248d68a1a081819d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41b1e734f151a88ccb702148615db27d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5ab6e54fc0c6b846c8d860860c087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db1cd89b86c99ce96a9336eb3b09c9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be594c4e8c6693571d71fa7c1951796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27a7cf91ca4cddeef99e8873ecc6fc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05932f1afdfa963def3c811591eb62bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d69dab2a6743011b461f62448890316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c21920a0a39b1604e130601f061b056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eab8e66f785800a153d34421b2e5540.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19a22804cdf4a90edff02dbb01b7481b.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e23c7e4c34891b3435c39f4989470ccf.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac852f327effde190b9ebf3dd08e037c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85f7e488464e41e1a1e1eed427154aa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aefd06c239145a2b6ae87a955aa51414.png)
(2)对于一个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e363087dcbe11e11a9ec545570735c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94fcc44ac04f54d5fcc1a6154b8b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac852f327effde190b9ebf3dd08e037c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2772cf7495c2c4c70086e7d936752d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b3c80a2adf39204ce112bda7115bf40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c8af44e1a8c05007f2137fa2d1907db.png)
您最近一年使用:0次
2024-03-26更新
|
548次组卷
|
5卷引用:山西省太原师范学院附属中学2023-2024学年高一下学期3月质量检测数学试题
名校
4 . 设函数
,其中a为实数.
(1)当
时,求
的单调区间;
(2)当
在定义域内有两个不同的极值点
时,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb835361d74631772eee26cf9cd5b0f1.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa4790fbf12830c009aa2c0d4dd3a8f.png)
您最近一年使用:0次
2024-03-03更新
|
987次组卷
|
6卷引用:山西省太原市成成中学校2023-2024学年高二下学期4月月考数学试题
山西省太原市成成中学校2023-2024学年高二下学期4月月考数学试题广东省2024届高三下学期2月大联考数学试题江苏省常州市奔牛高级中学2023-2024学年高二上学期第一次阶段调研数学试题(已下线)2023-2024学年高二下学期期中复习解答题压轴题十七大题型专练(1)(已下线)云南、广西、贵州2024届“3+3+3”高考备考诊断性联考(二)数学试题变式题16-19河北省石家庄二中润德中学2023-2024学年高二下学期第一次月考数学试题
解题方法
5 . 已知椭圆
:
的离心率为
,且过点
,经过右焦点
的直线
(斜率不为0)与椭圆
分别交于
、
两点.
(1)求椭圆
的方程;
(2)记椭圆
的左、右顶点分别为
,
,
和
的面积分别为
和
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)记椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c59c4295f918205f5598ecc9a96d8867.png)
您最近一年使用:0次
解题方法
6 . 已知函数
,
.
(1)当
时,求
的最小值;
(2)当
时,不等式
恒成立,求实数
取得的最大整数值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b40959c9c4afedb0cb831be6d42a989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2397df3279607612ea3cbef101ee0bf3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3368388525e30cb7179909b03184eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
7 . 已知抛物线
的准线与
轴相交于点
,过抛物线
焦点
的直线与
相交于
两点,
面积的最小值为4.
(1)求抛物线
的方程;
(2)若过点
的动直线
交
于
,
两点,试问抛物线
上是否存在定点
,使得对任意的直线
,都有
.若存在,求出点
的坐标;若不存在,则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e6c830bfa9a1b979a1a9665166424bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4c625a55ef1d2920a0605d52c8da23.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb7e4220a3e735e00249088888e0f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3835e6398d18d162afebc92cd2ae9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2024-01-26更新
|
256次组卷
|
2卷引用:山西省太原市2024届高三上学期期末学业诊断数学试题
名校
8 . 如图,在三棱锥
中,侧面
底面
,
,
是边长为2的正三角形,
,
分别是
的中点,记平面
与平面
的交线为
.
平面
;
(2)设点
在直线
上,直线
与平面
所成的角为
,异面直线
与
所成的角为
,求当
为何值时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829a1a887ceba13dd8551b1e3604bf6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9df740160690029ac1e730c85f20347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4820decdfaf6808eda1b625cc8aa0110.png)
您最近一年使用:0次
2024-06-10更新
|
574次组卷
|
8卷引用:山西大学附属中学校2023届高三下学期3月模块诊断数学试题
山西大学附属中学校2023届高三下学期3月模块诊断数学试题湖南师范大学附属中学2022届高三下学期月考(七)数学试题重庆市第八中学2022届高三下学期调研检测(七)数学试题云南省红河州建水实验中学2022-2023学年高一下学期4月考试数学试题(已下线)专题03 空间向量求角度与距离10种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)湖北省宜荆荆2024届高三下学期五月高考适应性考试数学试题 江苏省南通一中2023-2024学年高二年级数学下学期第二次月考(含答案)(已下线)立体几何与空间向量-综合测试卷B卷
9 . 已知函数
,函数
是
的反函数.
(1)若
的值域为
,求实数
的取值范围;
(2)是否存在实数
,便得函数
在
上的值域为
?若存在,求出实数
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cc82c265dd9669c5ef3e32ba17471f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00aefe8f4cf676d05ba6fb0303bc032.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01520356d39e4bd793fc4f16a284219e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f0dbc7a1166bd79a9b52d3c59e6a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
10 . 已知函数
(
)是偶函数.
(1)求k的值;
(2)若函数
(
),是否存在实数m,使得
的最小值为0?若存在,求出实数m的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db976f290e760aafd43e7e0b513383ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aff8d9b6533ff319420cdc5e8740b04.png)
(1)求k的值;
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c30337e2a643b0028f5e7fbbc2d7c1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e46371f310e03a153a1698aad9d4c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
您最近一年使用:0次