名校
1 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4749985beebb82af49bf81daed263b91.png)
在区间
上的最大值为
,最小值为
,记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764252096a427d22e7806422c0bff54f.png)
;
(1)求实数
、
的值;
(2)若不等式
对任意
恒成立,求实数
的范围;
(3)对于定义在
上的函数
,设
,
,用任意的![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
将
划分为
个小区间,其中
,若存在一个常数
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29258a85f75b9cb8b0f950d270165f84.png)
恒成立,则称函数
为
上的有界变差函数;
①试证明函数
是在
上的有界变差函数,并求出
的最小值;
②写出
是在
上的有界变差函数的一个充分条件,使上述结论成为其特例;(不要求证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4749985beebb82af49bf81daed263b91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf8197e4f3fd18815045d29c357a863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a248e47163191168a1b363937eebd618.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764252096a427d22e7806422c0bff54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3210274e57cc0487a58b99ea274b8aa1.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c5e6b1cf8b9ace30d26f232da3dac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)对于定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1ed40a8f67e93401e544284ceaaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc272934625d1232ad34eedc6b23267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752c287b0680a053e18be60f6e34ebba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97ea8f47d8d8d9e1832d52b1c7425450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1b6d5c6b222d95759ea7d39f0b908f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b09511efe31176effed50209b4aa5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29258a85f75b9cb8b0f950d270165f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fc2920f7b5d960d1a927fed29b6a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb1ed40a8f67e93401e544284ceaaf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
①试证明函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da34ce730f711c09909d53806fe2330a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
②写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627565d32e529cafcd2744d006ec6de2.png)
您最近一年使用:0次
2020-01-07更新
|
446次组卷
|
2卷引用:上海市控江中学2016-2017学年高三上学期第一次月考数学试题
名校
2 . 已知函数
,且
是定义在
上的奇函数.
(1)求实数t的值并判断函数
的单调性(不需要证明);
(2)关于x的不等式
在
上恒成立,求实数b的取值范围;
(3)若
在
上有两个零点
,求证:
且
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3b9e381cee106c590bfbd7ee5f8ecb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d09e8117906e8d3b634e04dd6ea010e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
(1)求实数t的值并判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)关于x的不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b99aad5444a5ae8f6ede73df2796bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa40b8865fc6621f349fcce91f1b1924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8938db94f49dcbe0c383fba0241bb0da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7e88a0a0bb2f88f38633b18a3cd158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b5cbd907176f31048cf8d07ef56323.png)
您最近一年使用:0次
2020-01-09更新
|
538次组卷
|
2卷引用:天津市滨海新区2019-2020学年高一上学期期末数学试题
12-13高一上·北京·期中
3 . 定义在
上的函数
,如果满足:对任意
,存在常数
,都有
成立,则称
是
上的有界函数,其中
称为函数
的上界.
(1)判断函数
是否是有界函数,请写出详细判断过程;
(2)试证明:设
,若
在
上分别以
为上界,求证:函数
在
上以
为上界;
(3)若函数
在
上是以
为上界的有界函数,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aea232de27d21a2646fd4520ea0726bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ee2d6f5c82efb89f3ebe7857bbe19.png)
(2)试证明:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd7bba058b2e191718d59debbe97a73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8fd1e808e015f4cb43d2e3a0529ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aae37cac299cbe3ccac181b2175287f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae0f8520349250a31be6d58542ef2d9.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a18264722215b39ab53a098fd18bded.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
4 . 已知函数
.
(1)判断函数
的奇偶性并证明;
(2)若方程
有且仅有一个实数根,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2095e0ae1814ec8adce10e65d534b0d0.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7a2ecd4ee71932cb6dd8200fd37c519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
5 . 已知
,
(1)若函数
与
在
时有相同的值域,求
的取值范围;
(2)若方程
在
上有两个不同的根
,求
的取值范围,并证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e14c2f347403fb0f36d1549d10ab9f4.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b1d358875baefff9736f2f31c2e28e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae8b0843577a84645d1887c7136e9305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad80c4ba8c593c5edfb167ae4a5f50f5.png)
您最近一年使用:0次
名校
6 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03d4fd9d26992f3569b43a3a68bbcea.png)
在
上为奇函数,
,
.
(1)求实数
的值并指出函数
的单调性(单调性不需要证明);
(2)设存在
,使
成立,求出
所在的集合
;
(3)请问是否存在
的值,使
最小值为
,若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03d4fd9d26992f3569b43a3a68bbcea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854c384242ea1b47496df067cc782521.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)设存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb63478132d4c1fef3c17e591919da83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ebd84a77eb6fb88506b1d80416a0194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)请问是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b4511aee0571fe27c8a6b04a5eae68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459c84c9addfbd1cdd0a877ba7c584e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2023-03-28更新
|
615次组卷
|
2卷引用:安徽省六安市第二中学2022-2023学年高一上学期期末考试数学试题
名校
解题方法
7 . 已知一动圆经过点
,且在
轴上截得的弦长为4,设动圆圆心的轨迹为曲线
.
(1)求曲线
的方程;
(2)过点
任意作相互垂直的两条直线
,分别交曲线
于不同的两点
和不同的两点
.设线段
的中点分别为
.
①求证:直线
过定点R,并求出定点R的坐标;②求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f36374ce95a4945d0e58264c2b271f.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764c199d659322854377a92fee97642d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
①求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
您最近一年使用:0次
2022-04-06更新
|
318次组卷
|
3卷引用:四川省泸州市泸县第五中学2021-2022学年高二下学期第一学月(3月)考试文科数学试题
8 . 已知函数
,
.
(1)若
,求函数
在
的值域;
(2)若
,求证
.求
的值;
(3)令
,则
,已知函数
在区间
有零点,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dfc59e88149b506865a18f249c56f68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a768cc949e4d1ca3effaa7f82b2156.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926b791b23dce655cb9230b416c0c42a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66ef59c3970f3581a5ea29e21fd564d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e4e14e7cce3bcd0371d32858b0a2c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ef502f2520c255f8c7281e343ce2357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdaaf67e089d2dd8468fbaba13d01b52.png)
(3)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a80661feb5630831d21c3d7a328c17ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc38c68db969c0a77847417bdc732d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e593828316139a54019e352dec883f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dccf1f9faac56117d6d3dd1dddd286d.png)
您最近一年使用:0次
2022-06-24更新
|
2766次组卷
|
4卷引用:四川省德阳市第五中学2021-2022学年高一下学期6月月考文科数学试题
9 . 设函数
,定义集合
,集合
.
(1)若
,写出相应的集合
和
;
(2)若集合
,求出所有满足条件的
;
(3)若集合
只含有一个元素,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce5b409bb706df9ca1ccb27f893e2b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0f90056bdaa86e0b862bde3dce36b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a0c740c333f153ae2e9cdef157686b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8897aa03f96629b56ab1cc6c2398bb30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b5886cf72ed5a1073263eb9ff485c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b864bba6e36f6577c74799bb1c63303.png)
(2)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e76fcf1fb1bae5bfeb45951da12efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cd5371a6f0f82c65dd22f75f8b807c1.png)
(3)若集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b864bba6e36f6577c74799bb1c63303.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a0bf834a9b75cdc4f9e868cd76e78e.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,在六面体
中,
是等边三角形,二面角
的平面角为30°,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/abf1f59c-1ce0-42f8-a29a-432634afd36b.png?resizew=215)
(1)证明:
;
(2)若点E为线段BD上一动点,求直线CE与平面
所成角的正切的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1e3a43d0fa18f6c0888ba804d5b329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f479b251fdb01bae6d16abb7f2d694a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0b3c477034d1974fecb5875c557fef6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/abf1f59c-1ce0-42f8-a29a-432634afd36b.png?resizew=215)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c583493109d50c9e4634c05e9042a9f.png)
(2)若点E为线段BD上一动点,求直线CE与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
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2022-06-23更新
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7卷引用:浙江省宁波市镇海中学2021-2022学年高二下学期期末数学试题
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