名校
解题方法
1 . 已知奇函数f(x)
,函数g(θ)=cos2θ+2sinθ
,θ∈[m,
].m,b∈R.
(1)求b的值;
(2)判断函数f(x)在[0,1]上的单调性,并证明;
(3)当x∈[0,1]时,函数g(θ)的最小值恰为f(x)的最大值,求m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de511e0b722a4b84a3ca7fd28cfc39ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575fdebc8f8ad46f80ec388e1784ee23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01e09bd8b1da7682ac91bc14552870e0.png)
(1)求b的值;
(2)判断函数f(x)在[0,1]上的单调性,并证明;
(3)当x∈[0,1]时,函数g(θ)的最小值恰为f(x)的最大值,求m的取值范围.
您最近一年使用:0次
2020-03-04更新
|
436次组卷
|
2卷引用:江苏省无锡市江阴市2019-2020学年高一上学期期末数学试题
名校
2 . 已知函数
(
,
).
(1)若函数
的图象与直线
均无公共点,求证:
;
(2)若
,
时,对于给定的负数
,有一个最大的正数
,使
时,都有
,求
为何值时
最大?并求
的最大值;
(3)若
,且
,又
时,恒有
,求
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce086037087f58409a28b4885979fd77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0e9d1ad9561d693958756ee8398218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3051f43ac48c0a730a791b8a93ad37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abffa1d225ca1e8bd2d15ab6d3ad9a50.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3320a13248a3a1208ff6ee85c9d26f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9439d9d9bc4f93dce4b94d1e33e06bec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f804646698060703c5458ff5637c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/044934f7dbd6847a30f13a34c9bb4e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efdb19e1863e40b863519bca9edcdf33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f804646698060703c5458ff5637c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760f804646698060703c5458ff5637c7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77cdb8806a697e8e5480fad9c380baa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fdf1eec5487c094e8d38cbc77b91604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
您最近一年使用:0次
名校
3 . 已知
,
是实常数.
(1)当
时,判断函数
的奇偶性,并给出证明;
(2)若
是奇函数,不等式
有解,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4b013905ff4d8e910fb3f82cbf2b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d4d4729d3d07d665c785bd8befabecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-02-05更新
|
652次组卷
|
3卷引用:江苏省南京市江宁区2018-2019学年高一下学期期末数学试题
江苏省南京市江宁区2018-2019学年高一下学期期末数学试题福建省厦门市湖滨中学2020-2021学年高一上学期期中考试数学试题(已下线)练习7+幂函数、指数函数、对数函数图像与性质-2020-2021学年【补习教材·寒假作业】高一数学(北师大版)
解题方法
4 . 定义在R上的函数f(x)=|x2﹣ax|(a∈R),设g(x)=f(x+l)﹣f(x).
(1)若y=g(x)为奇函数,求a的值:
(2)设h(x)
,x∈(0,+∞)
①若a≤0,证明:h(x)>2:
②若h(x)的最小值为﹣1,求a的取值范围.
(1)若y=g(x)为奇函数,求a的值:
(2)设h(x)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0147d162096a74c7a507e7ca37d816.png)
①若a≤0,证明:h(x)>2:
②若h(x)的最小值为﹣1,求a的取值范围.
您最近一年使用:0次
2020-02-01更新
|
275次组卷
|
2卷引用:浙江省温州市普通高中2018-2019学年高一下学期期末(A卷)数学试题
名校
解题方法
5 . 已知函数
(
且
).
(1)求函数
的定义域,并求出当
时,常数
的值;
(2)在(1)的条件下,判断函数
在
的单调性,并用单调性定义证明;
(3)设
,若方程
有实根,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289cf9906f4301f108fa50b991298e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c400a615a16a1662de98dfb4e49d58d3.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/752a12112e7a21c08f76ee99f7bf188c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)在(1)的条件下,判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a51a03f3e4d8e559b9850e4222c463.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff1b756c50cb308aeeb77accb9c10815.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1efbe3b46023d8fbfd4a78902ff9c25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2020-03-04更新
|
429次组卷
|
2卷引用:广东省汕头市金山中学2019-2020学年高一上学期期中数学试题
6 . 已知数集
,其中
,且
,若对
,
与
两数中至少有一个属于
,则称数集
具有性质
.
(1)分别判断数集
与数集
是否具有性质
,说明理由;
(2)已知数集
具有性质
,判断数列
,
,…,
是否为等差数列,若是等差数列,请证明;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ea7fcdb5423c1c8c032a3efcf245682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c1d125b49fe60bc9796cf7d72e9170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bcfc48f9bc23cc43085bdb910e7a136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550e79a4d9c549c9e28bbf30f74e24d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3541598c0e0e6d5050c5a562515c430e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13ee542834ccbb57fcc55b1680ca9db.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/dad2a36927223bd70f426ba06aea4b45.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1906b96e054c5e74d295b61149a36b4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ef5ce9b1b2850e4a95e7c0ce44bac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)已知数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7152dfaf58cc9ff3df8c3d1ac7c435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7da2f386b78cdf6489efaa2f5820d3e.png)
您最近一年使用:0次
解题方法
7 . 已知函数
.
(1)当
时,求函数
的极值;
(2)当
时,证明:在
上
存在唯一零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995d35b828405b748236fde21520c6f9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f4c78214e43a8b93f2a57072033cbcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
解题方法
8 . 已知定义在R上的偶函数
和奇函数
满足:
.
(1)求
,
并证明:
;
(2)当
时,不等式
恒成立,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff79c1ecb223a367f035c1d51ba3dfc9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e2e6c1590ef1122f4e6ace4852890a2.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b35e246b7e91445c1412f28c056ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d1077b66e5e7ea591c05b4a7e0e0567.png)
您最近一年使用:0次
2020-02-14更新
|
547次组卷
|
2卷引用:安徽省宣城市2019-2020学年高一上学期期末数学试题
名校
解题方法
9 . 已知
是定义在
上的奇函数,且
,当
,且
时,有
成立.
(1)判断
在
上的单调性,并给予证明;
(2)若
对任意的
以及任意
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a547418f2bc38da0091f1a4a482fa5b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96bc2eeaca8a8ce4bcce2bff011a11bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d01645cf54dd71aa3d55f8f40c9bdaf.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417ab20883d799aaf311371393fa7d7c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a97087acd5f4a7c147c9ef41e67849a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/262d7da8f17131eef23addd1854b170d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f0ca536621ec8db02707ba65917029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-05-08更新
|
563次组卷
|
2卷引用:四川省双流中学2019-2020学年高一下学期开学考试数学试题
10 . 已知函数
,
.
(1)判断
的单调性,并证明之;
(2)若存在实数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
,使得函数
在区间
上的值域为
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6caf11fce0e5d3df0c9d7854b1e5bc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf039c46a25e331446c6ee1e9af3c82.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
(2)若存在实数
![](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/4a5862c0c90cc629fb509d93e6ab1ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f15eb7cd066e13367998a2da2653976.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2020-01-19更新
|
469次组卷
|
2卷引用:浙江省温州市2019-2020学年高一上学期期末数学试题(B)