1 . 已知函数
(
).
(1)指出
的单调区间;(不要求证明)
(2)若
,
,
,
满足
,
,
,且
(
,
,
),求证:
;
(3)证明:当
时,不等式
(
)对任意
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbf40041a26fe4539efc7185b45dcf53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
(1)指出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.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/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7ec808ad60dbf016632ec816eaca1df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3916e25d592d36e90fe4f35be72c43c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe72ccd2bee6a6e9d7199261b3e3da69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64c6bd88c09d6848101421a9564c19c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c45176df950dfe48b8ca7eac08ee349.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd69d26f76d5a55cf072fa49b53d437.png)
(3)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48adb8a59b5c02fad5eada1b35171cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d7482925b44b2d55a8d1c9b8fcc1be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28652e52c0b02a343e618935ea625cbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/813b9aa31af28f99d21fc0dc0c95475c.png)
您最近一年使用:0次
2 . 已知双曲线
,点
,经过点M的直线交双曲线C于不同的两点A、B,过点A,B分别作双曲线C的切线,两切线交于点E.(二次曲线
在曲线上某点
处的切线方程为
)
(1)求证:点E恒在一条定直线L上;
(2)若两直线与L交于点N,
,求
的值;
(3)若点A、B都在双曲线C的右支上,过点A、B分别做直线L的垂线,垂足分别为P、Q,记
,
,
的面积分别为
,问:是否存在常数m,使得
?若存在,求出m的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0017262e45089093f70001cae2c60257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363598fd39f2269952dc6ddd1201346c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f16f528223f178103c2d8193b45e07af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b4f86e48e2b0d63c1865c60ed1e4d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7444e40f6ef2b62a680fb325a266cb63.png)
(1)求证:点E恒在一条定直线L上;
(2)若两直线与L交于点N,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9619a20d8dfa7aeaefd5fc1b76b5a40c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
(3)若点A、B都在双曲线C的右支上,过点A、B分别做直线L的垂线,垂足分别为P、Q,记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c2b58424e893df4e01c912f87e09095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf173f2377cc32d2a33d889729a224e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca1f167ece5d18225840af97b39af9e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a22e8a68eb538caf433c0a280f6623.png)
您最近一年使用:0次
2024-02-05更新
|
1211次组卷
|
2卷引用:辽宁省大连市2023-2024学年高二上学期期末数学试题
3 . 双曲线
和
的方程均满足
,其中
的焦点在
轴上,顺次连接
的两个焦点和
的两个顶点恰好可以构成一个面积为4的正方形.
(1)求双曲线
和
的方程.
(2)若
为
左支上一动点且不在
轴上,过
作
的切线交
于
两点,过
作
的平行线交
于
,顺次连接
四点构成四边形
,求证:四边形
的面积为定值.
![](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/7d599c8a6dbf883077ac00dc5d00257c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2816c1cb72ed019c7a062bd59aab4af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2816c1cb72ed019c7a062bd59aab4af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5663f0992b845a51c65f0da3a0140c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d96e428931b19cf639d3e0f26ebe23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41d96e428931b19cf639d3e0f26ebe23.png)
您最近一年使用:0次
4 . 某企业为了调动员工工作的积极性,提高生产效率,根据员工每小时的生产速度发放奖金,经研究,该企业的奖金发放方案为:当员工生产速度为
千克/小时(生产条件要求
且匀速生产),其每小时可获得的奖金为
元.
(1)判断此奖金发放方案能否使员工每小时获得的奖金
随生产速度
(
)的增加而增加?并证明你的结论;
(2)某天,该企业安排员工甲生产72千克该产品,为获得更多的总奖金,该员工应该选取何种生产速度?并求此时获得的总奖金.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f6b0b4cc70998d6926e69050fc300c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee9bc853634078766bbb7fc8c12be99.png)
(1)判断此奖金发放方案能否使员工每小时获得的奖金
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f6b0b4cc70998d6926e69050fc300c8.png)
(2)某天,该企业安排员工甲生产72千克该产品,为获得更多的总奖金,该员工应该选取何种生产速度?并求此时获得的总奖金.
您最近一年使用:0次
解题方法
5 . 已知函数
.
(1)若
时,求
的定义域;
(2)若函数
的图像关于直线
对称.
①求a,b的值;
②求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9453acce2c4269123931aa2f501442c2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3440745ce66413cd501dbabeff44cd60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b334dafda377c3db77647c8cf1e95f.png)
①求a,b的值;
②求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfcdbfa315aa31287588d98cdfaddf3.png)
您最近一年使用:0次
名校
解题方法
6 . (1)已知函数
及其导函数
的定义域均为
,设
是曲线
在点
处的切线的方程. 证明:当
是增函数时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
(2)已知
,设
的最大值为
,证明:
.
(参考数据:
,
,
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c4f6388b5809b156ce9289dc5846920.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38da3eb873f57196dc4fda166a1db16e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/447d6f62c09c1d05346fd16a24159f6e.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5b440818076e1e7fa8800fa848ae06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08320e6e96f872f1fcf6ad8096ebaa10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f01a1e17f4bd23682465df5b42309725.png)
(参考数据:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06341cc14870ff71931aae0d3d78abfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ebbae545ae1e8e4b06bf861fa53e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a2f2d080ac398bea650aecd40ca8ab.png)
您最近一年使用:0次
7 . 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)
您最近一年使用:0次
2023-12-14更新
|
942次组卷
|
6卷引用:辽宁省大连市2022-2023学年高一上学期期末数学模拟试题
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(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
名校
解题方法
8 . 已知幂函数
,
(1)求
的值;
(2)若_________写出函数
的单调区间(不需证明单调性),并利用
的单调性解不等式
.
①函数
为奇函数;②函数
为偶函数,从这两个条件中任选一个填入横线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b785be7d800df095d215cfda2b2ad8c8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若_________写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2212fb0e316382c889cc409d3259afce.png)
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
9 . 已知大气压强
(帕)随高度
(米)的变化满足关系式
是海平面大气压强.
(1)世界上有14座海拔8000米以上的高峰,喜马拉雅承包了10座,设在海拔4000米处的大气压强为
,求在海拔8000米处的大气压强(结果用
和
表示).
(2)我国陆地地势可划分为三级阶梯,其平均海拔如下表:
若用平均海拔的范围直接代表海拔的范围,设在第二级阶梯某处的压强为
,在第三级阶梯某处的压强为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3de17a73e40a55e7e930bbbec3de1d0.png)
(1)世界上有14座海拔8000米以上的高峰,喜马拉雅承包了10座,设在海拔4000米处的大气压强为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a886d45a46bdde67115c5911cb85ea6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3606c4a853a6a34cb7f33bea81b15a1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a886d45a46bdde67115c5911cb85ea6.png)
(2)我国陆地地势可划分为三级阶梯,其平均海拔如下表:
平均海拔(单位:米) | |
第一级阶梯 | ![]() |
第二级阶梯 | ![]() |
第三级阶梯 | ![]() |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adad9633b73dfbbb3d84b4f15979e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845e602f8f75a107f186e4803ecafa05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c0b5136e09293a4488211b80ba86ee.png)
您最近一年使用:0次
2023-07-29更新
|
129次组卷
|
2卷引用:辽宁省部分学校2022-2023学年高二下学期期末联考数学试题
名校
解题方法
10 . 如图①在平面直角坐标系
中,已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9366a89d9d925fc623a308a5c5eed30e.png)
,
,动点
在线段
上.
(1)求
的最小值;
(2)以四边形
为底面做四棱锥
如图②,使
平面
,且
,求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9366a89d9d925fc623a308a5c5eed30e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/513eafd10fa1ec0196562865517e0b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ef8f34e64439c14ec2d8bab581906d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/2/96167441-f610-4722-9679-12b00d193fdd.png?resizew=335)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f524ec18dd8fc2f572a9b1ce532395cd.png)
(2)以四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b81a6235ef96041dbf59ac50e6e5f86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f3280cd6719ad73e7e6ab77248baa29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cbddc9b1f36e2cabd9a6c830d14736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc83f34b5a3c1dc09d990ce4bdc8e078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/882292451ed3fca6df1e925d12377f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bf006d9cf9568dd567c25fd20a0c85.png)
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