解题方法
1 . 已知函数
.
(1)当
时,求
的最大值;
(2)若
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f60b57fb4365b00a895261df37c64514.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6acb0f1ac694dd177e99fc385f23318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2024-01-09更新
|
1329次组卷
|
5卷引用:甘肃省武威市2024届高三上学期阶段调考数学试题
甘肃省武威市2024届高三上学期阶段调考数学试题辽宁省辽阳市2024届高三上学期期末数学试题(已下线)专题2-7 导数压轴大题归类-1(已下线)模块三 大招11 隐零点代换(已下线)专题10 导数12种常见考法归类(4)
解题方法
2 . 已知函数
,且
的图象过点
.
(1)求
的值及
的定义域;
(2)求
在
上的最小值;
(3)若
,比较
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d9e309d8ed5a5d30390673a5361733d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37fa1476cf3552b9ae91ef039b1c6c80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15ad1d8d2459b942a3d59f52b437e55d.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4812103615c89baad99e6c37f940f1af.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6317108a616314b8a47357f283e5fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483d738422dd61c4d4bef79e2427dd58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0b020ba0fb9f2bf0ebe9a8217a9c89.png)
您最近一年使用:0次
3 . 已知椭圆
的离心率
,短轴长为
.
(1)求椭圆
的方程;
(2)过点
且斜率不为
的动直线
与椭圆
交于
、
两点,点
是直线
上一定点,设直线
、
的斜率分别为
、
,若
为定值,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/081cd41dab0f2a8f84b0e9f1df4843fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d585d2d6643471640905d234d9538c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
名校
解题方法
4 . 某区域市场中
智能终端产品的制造全部由甲、乙两公司提供技术支持.据市场调研及预测,
商用初期,该区域市场中采用的甲公司与乙公司技术的智能终端产品各占一半,假设两家公司的技术更新周期一致,且随着技术优势的体现,每次技术更新后,上一周期采用乙公司技术的产品中有
转而采用甲公司技术,采用甲公司技术的产品中有
转而采用乙公司技术.设第
次技术更新后,该区域市场中采用甲公司与乙公司技术的智能终端产品占比分别为
和
,不考虑其他因素的影响.
(1)用
表示
,并求使数列
是等比数列的实数
.
(2)经过若干次技术更新后,该区域市场采用甲公司技术的智能终端产品的占比能否达到
以上?若能,则至少需要经过几次技术更新;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b27772ded41cb6beecf19d5da91e82a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b27772ded41cb6beecf19d5da91e82a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3eb7c16bd2a184286db865b73ae3c0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28555fa2f3a09261cb4e0305d390145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/686ece75006ad358f23314dc8a246e11.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96abfe2da27a63e6affb19a0c80236d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/090426eb29836bc30c006b3739c08057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28f7e6b0bbb5f64834eae98e868a6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)经过若干次技术更新后,该区域市场采用甲公司技术的智能终端产品的占比能否达到
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a263874aa2031f847d06d6cef24aea.png)
您最近一年使用:0次
2024-01-03更新
|
541次组卷
|
5卷引用:甘肃省白银市靖远县第四中学2023-2024学年高二上学期1月期末考试数学模拟试题
甘肃省白银市靖远县第四中学2023-2024学年高二上学期1月期末考试数学模拟试题重庆市乌江新高考协作体2024届高三上学期高考第一次联合调研抽测数学试题(已下线)考点8 等差、等比数列的实际应用 2024届高考数学考点总动员(已下线)考点11 由实际问题探究递推关系 2024届高考数学考点总动员(已下线)1.3.1 等比数列7种常见考法归类(3)
名校
5 . 已知抛物线
过点
.
(1)求抛物线C的焦点到准线的距离.
(2)已知点
,过点
的直线l交抛物线C于点M、N,直线
分别交直线
于点P、Q,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37ab7408ffcefcb8e5e1ad4a9c58f1b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941a1c49b132e8295d3cb92542befce5.png)
(1)求抛物线C的焦点到准线的距离.
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95e84f5c91c910aaafc5e74dbfbdf59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee07d86765c4fb74ac647742f16bd57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d075e1f6049129308db0cc58e3916e71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15d9d3102e916e7f1900b39f4b8b2868.png)
您最近一年使用:0次
名校
解题方法
6 . 在平面直角坐标系
中,双曲线
的左、右焦点分别为
的离心率为2,直线
过
与
交于
两点,当
时,
的面积为3.
(1)求双曲线
的方程;
(2)已知
都在
的右支上,设
的斜率为
.
①求实数
的取值范围;
②是否存在实数
,使得
为锐角?若存在,请求出
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/704bfc280d817fb77006ee98d4d7e5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05739577d493cc19852de143d8793670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42fc33bcfc63ec2f4940ccd3f862400.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②是否存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27935c1ef4df2d52ac697678a3c8f39d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-08-18更新
|
2867次组卷
|
8卷引用:甘肃省武威市四校联考2024届高三上学期新高考备考模拟(开学考试)数学试题
甘肃省武威市四校联考2024届高三上学期新高考备考模拟(开学考试)数学试题(已下线)考点19 解析几何中的探索性问题 2024届高考数学考点总动员【练】广东省2024届高三数学新改革适应性训练二(九省联考题型)(已下线)最新模拟重组精华卷1-模块一 各地期末考试精选汇编湖北省黄冈市浠水县第一中学2024届高三下学期第一次高考模拟数学试题(已下线)(新高考新结构)2024年高考数学模拟卷(二)广东省云浮市云安区云安中学2024届高三下学期3月模拟考试数学试题上海市闵行中学2024届高三下学期4月月考暨二模模拟考试数学试卷
7 . 已知椭圆
的左顶点为
,过
作两条互相垂直的直线
且分别与椭圆
交于
两点(异于
点),设直线
的斜率为
,
为坐标原点.
(1)用
表示点
的坐标;
(2)求证:直线
过定点;
(3)求
的面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893d4e8d70ea2c716ac7b6c1777a77f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
您最近一年使用:0次
解题方法
8 . 在平面直角坐标系
中,已知圆
和圆
.
(1)若直线
过原点,且被圆
截得的弦长为6,求直线
的方程;
(2)是否存在点
满足过点
的无穷多对互相垂直的直线
和
,它们分别与圆
和圆
相交,且直线
被圆
截得的弦长与直线
被圆
截得的弦长相等?若存在,求出点
的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9131b2f6321413496907b3ca5ae62ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132d4325a8e3a7366411bd849cd0d673.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
名校
解题方法
9 . 已知抛物线
,垂直于
轴的直线
与圆
相切,且与
交于不同的两点
.
(1)求p;
(2)已知
,过
的直线与抛物线
交于
两点,过
作直线
的垂线,与直线
分别交于
两点,求证:
.
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d7f565360cb8de963874291c7013118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61e0c0b5bda80a9aa5b49b03ce2f9352.png)
(1)求p;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a42451bdbef6c82dbaf8e06f0614794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a225b6550530973e4859ea29765c728a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a225b6550530973e4859ea29765c728a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe7fd9b0c3c203a053a7ea52b71e7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a36d2f86d8560ef6a67a34cecb81494b.png)
您最近一年使用:0次
2023-12-29更新
|
286次组卷
|
3卷引用:甘肃省张掖市高台县第一中学2024届高三下学期模拟考数学试题
名校
10 . 已知函数
有两个零点.
(1)求
的取值范围;
(2)设两零点分别为
,证明
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a72d15c3f47f19ef0d28147fc264a70.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设两零点分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aca579894dad67bc82cb715fd48e0d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f93f6d13fd7f0f208459faa0685cc81e.png)
您最近一年使用:0次
2023-12-29更新
|
262次组卷
|
2卷引用:甘肃省张掖市高台县第一中学2024届高三下学期模拟考数学试题