1 . 已知定义域为
的函数
,其图象是连续的曲线,且存在定义域也为
的导函数
.
(1)求函数
在点
的切线方程;
(2)已知
,当
与
满足什么条件时,存在非零实数
,对任意的实数
使得
恒成立?
(3)若函数
是奇函数,且满足
.试判断
对任意的实数
是否恒成立,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851c68ef2e0703706f3b528daa902eb8.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d0d5f2bae6b38d6877b8b40865e834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3832d863e6cefdfe45cff4319e1fbdb.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a48a3e7a13ec19e1ba5ba54e520c76df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e06618e1fff402ca9269e10a396532f.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e084f839e9b7a03fea8b0b596674fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ddc12af8da0819a120eaae5858c4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2024·全国·模拟预测
解题方法
2 . 行列式是近代数学中研究线性方程的有力工具,其中最简单的二阶行列式的运算定义如下:
.
(1)在等比数列
中,
是
的两个实根,求
的值;
(2)已知数列
的前
项和为
,且
,若
,求数列
的前
项和;
(3)已知
是奇函数,
是偶函数.设函数
,且存在实数
,使得
对于任意的
都成立,若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7875027c38205a2c081ce94d03eb8a91.png)
(1)在等比数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd7e6d752e48eb8af83280240656536f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb1202fdf29e802a34482992c54ac42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f054edb48ce3c81c42d34c63935f13c4.png)
(2)已知数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a724176ea8a89723acf950b544aa9d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9666bad945b494468ca2e719a5038c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e15c2171c1be9ec394494ad822a048d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32de19d853a1c2b9e1de56a56acf1dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9da4fdfdddc259dcef9fdd4b826b64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db43f7f1ca236145e73aa8cbbc17c825.png)
您最近一年使用:0次
名校
解题方法
3 . 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
名校
解题方法
4 . 已知实数a满足
,
.
(1)求实数a的取值范围;
(2)若
,
,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bc7e2758fd2002fbeaef52ab14a8e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618ddbf4f91ffd36c5cedede3802e8d5.png)
(1)求实数a的取值范围;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd0d5ef0170d4d4dc056eed669807ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95f293ebe90eaabc460d2e2713e4ab48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe653ed86488f8dcdf2612ac544fe2aa.png)
您最近一年使用:0次
5 . 构造出3个不同的偶函数.
您最近一年使用:0次
6 . 如图,已知
是偶函数,
(1)将上图补充完整;
(2)写出
的单调区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/8/957483ac-69b0-4ded-bf10-3a5bcd40ca64.png?resizew=184)
(1)将上图补充完整;
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2023-08-06更新
|
135次组卷
|
2卷引用:广东省佛山市南海区2022-2023学年高一上学期期中数学试题
解题方法
7 . 已知定义域为R的奇函数
最大值为2,在
上单调递增,在
单调递减,且当
时
,
(1)求函数
在
的单调性并证明;
(2)求函数
的最小值,并说明理由;
(3)直接写出函数
图象的对称中心坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6554ac3dff4a59833e407db887f6e6.png)
(2)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(3)直接写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55de1c1936c51ce70e19f6989ba68dc6.png)
您最近一年使用:0次
解题方法
8 . 已知
是定义域为
的偶函数.
(1)求
的最大值;
(2)从下面①②两个结论中任意选择一个证明,如果两个都证明,按第一个计分.
①
;
②
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8719faea5fc808567ea5cb663cf3b4e.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
(2)从下面①②两个结论中任意选择一个证明,如果两个都证明,按第一个计分.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfdda677a581df60e5178ceb77335ae5.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5b8224ba466ff97b3e1e42bc0c1529d.png)
您最近一年使用:0次
名校
9 . 已知函数
,定义![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee06216fbd39db30d6f2419da1ee02bf.png)
(1)写出函数
的解析式;
(2)若
,求实数
的值;
(3)已知函数
,集合
,集合
,
,若函数
是偶函数,写出所有满足条件的
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee06216fbd39db30d6f2419da1ee02bf.png)
(1)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f896f0c227d6dc7cb554f943f6b36ff5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8599e00396d36f610bc03f2469f9b5a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab93efd42a3054040ccff8adf697c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289090ab57054b891bc6c4ffc7c689cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6b46a8948ddfe69cc2d264d2f5f5aac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede280b7d4529ca9afb08bff174225ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda24a870698ed1ab24f987476d18d12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
2022-11-08更新
|
265次组卷
|
2卷引用:北京市第五十中学2022-2023学年高一上学期期中考试数学试题
名校
解题方法
10 . 已知函数
是偶函数(其中a,b是常数),且它的值域为
.
(1)求
的解析式;
(2)若函数
是定义在R上的奇函数,且
时,
,而函数
满足对任意的
,有
恒成立,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d794f10a4d0efe9aba0e98242f47333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c36c3781d5caf82f3749cd503d23ad6.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e541ea2f855f981c96207070683d388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c459c5d37f30210330dbeaf49f5662f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a04d5dedf90c054802fa63dfddbf53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b4ecaea942c9db398b401df1b324b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/056b0b36f15ae78b0ec18555cc5c0fce.png)
您最近一年使用:0次
2022-02-11更新
|
293次组卷
|
2卷引用:河南省信阳市信阳高级中学2021-2022学年高一上学期期末考试理科数学试题