1 . 已知函数
,其中
.
(1)求证:
是奇函数;
(2)若关于
的方程
在区间
上有解,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6715d2ec8dc06da5a0f796139c9b5a88.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
(2)若关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91d0383761cb327aae1d00f4b84d786.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f094b4fcb0df74103b78e478bd4448d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
2 . 已知函数
,其中
,实数
,下列选项中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3521e68e3d0a927c4281bb159b3c9534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4456675a5dbe545462a22cef9aca8fe.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若函数![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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解题方法
3 . 为了研究y关于x的线性相关关系,收集了5组样本数据(见下表):
若已求得一元线性回归方程为
,则下列选项中正确的是( )
x | 1 | 2 | 3 | 4 | 5 |
y | 0.5 | 0.9 | 1 | 1.1 | 1.5 |
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8498919ac0cc8a16477beaafec83c10d.png)
A.![]() |
B.当![]() |
C.样本数据y的第40百分位数为1 |
D.去掉样本点![]() |
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4 . 在下列函数中,值域为
的偶函数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
5 . 如图,两条足够长且互相垂直的轨道
相交于点
,一根长度为
的直杆
的两端点
分别在
上滑动(
两点不与
点重合,轨道与直杆的宽度等因素均可忽略不计),直杆上的点
满足
,则
面积的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d718b208bce3e2778a466b2ed8d5312f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532d9de08698f61d7c010805c61a4ec5.png)
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6 . 同时抛掷三枚相同的均匀硬币,设随机变量
表示结果中有正面朝上,
表示结果中没有正面朝上,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c0cd2d7ae8394a0fd6977c3e59401f.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71ce9db5574a2df6184bdc7cd13b208a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fef57584523e293a6f482bb4cf31c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c0cd2d7ae8394a0fd6977c3e59401f.png)
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解题方法
7 . 已知
的二项展开式中各项系数和为
,则展开式中常数项的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4beede409558bb4a50800bd80a358b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f5e8a53028fc78b08ba4787ef51e516.png)
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解题方法
8 . 若正数
满足
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663a61ad241d5d874c9a9362f0ee917c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f00f997ae12c30f551adb834e1d7ef8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b0113fd4c7d157757571f9a009e02af.png)
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9 . 在
中,
,
,
,则
的外接圆半径为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe31795796bc68d6803835d9a687b6bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d32220fd969663f42cd619f8cc8b355c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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10 . 已知复数
(
为虚数单位),则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca6c17df8a51bb6492426fddcfb622.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e63bbbcd3c5da945f537550cfa5cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca6c17df8a51bb6492426fddcfb622.png)
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