1 . 2020年新冠病毒爆发,许多志愿者积极参加抗疫活动.现有甲、乙两位志愿者同时徒步从A地出发赶往C地,甲不经B地直接匀速前往C地,他的速度(单位:千米/小时)范围由函数
决定:乙经B地接人后前往C地,速度为8千米/小时,此间在B地停留15分钟,其中AC=5千米,AB=4千米,BC=2千米,如图.
![](https://img.xkw.com/dksih/QBM/2020/7/27/2515068841705472/2515147582939136/STEM/7812f4d9763c4e9e807f51b8a1a747c4.png?resizew=228)
(1)求v(x)的取值范围;
(2)若甲以最快速度赶往C地,且志愿者的对讲机的有效通话距离是3千米,试问这一路上甲、乙两人的对讲机是否能正常通话?请说明理由.
(3)甲、乙到达C地后原地等待,为使两位志愿者在C处互相等待的时间不超过1小时,甲的速度v(x)中x应控制在什么范围内?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a7fcd9353491f1a674533dac241ddea.png)
![](https://img.xkw.com/dksih/QBM/2020/7/27/2515068841705472/2515147582939136/STEM/7812f4d9763c4e9e807f51b8a1a747c4.png?resizew=228)
(1)求v(x)的取值范围;
(2)若甲以最快速度赶往C地,且志愿者的对讲机的有效通话距离是3千米,试问这一路上甲、乙两人的对讲机是否能正常通话?请说明理由.
(3)甲、乙到达C地后原地等待,为使两位志愿者在C处互相等待的时间不超过1小时,甲的速度v(x)中x应控制在什么范围内?
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2 . 已知函数
的图像经过点
及![](https://img.xkw.com/dksih/QBM/2016/9/6/1572999335944192/1572999341801472/STEM/afcd162c07a24285b6d03be16c738e1c.png)
(1)已知
时,
恒成立,求实数
的取值范围;
(2)当
取上述范围内的最大整数值时,若有实数
,使得
对于
恒成立,求
的值.
![](https://img.xkw.com/dksih/QBM/2016/9/6/1572999335944192/1572999341801472/STEM/a9753afc4ec9497ab4ea72417480c117.png)
![](https://img.xkw.com/dksih/QBM/2016/9/6/1572999335944192/1572999341801472/STEM/a005f371287e40468492bbbaafe43af0.png)
![](https://img.xkw.com/dksih/QBM/2016/9/6/1572999335944192/1572999341801472/STEM/afcd162c07a24285b6d03be16c738e1c.png)
(1)已知
![](https://img.xkw.com/dksih/QBM/2016/9/6/1572999335944192/1572999341801472/STEM/07362fce4e25494cadacf2425b835593.png)
![](https://img.xkw.com/dksih/QBM/2016/9/6/1572999335944192/1572999341801472/STEM/f9af49d09878472cb85362e63b1c2a54.png)
![](https://img.xkw.com/dksih/QBM/2016/9/6/1572999335944192/1572999341801472/STEM/abb3062e2f984056b731c0c26a8fc69a.png)
(2)当
![](https://img.xkw.com/dksih/QBM/2016/9/6/1572999335944192/1572999341801472/STEM/abb3062e2f984056b731c0c26a8fc69a.png)
![](https://img.xkw.com/dksih/QBM/2016/9/6/1572999335944192/1572999341801472/STEM/024ac4272c464059931835d301b5b677.png)
![](https://img.xkw.com/dksih/QBM/2016/9/6/1572999335944192/1572999341801472/STEM/51addacc3a1245328b35decc2ca4f4d8.png)
![](https://img.xkw.com/dksih/QBM/2016/9/6/1572999335944192/1572999341801472/STEM/74a13c911e364fac858915ac293619d5.png)
![](https://img.xkw.com/dksih/QBM/2016/9/6/1572999335944192/1572999341801472/STEM/61b482eb24e348bb85193abfd27a844e.png)
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3 . 已知函数
(
为常数且
).
(1)若函数的定义域为
,值域为
,求
的值;
(2)在(1)的条件下,定义区间
,
,
,
的长度为
,其中
,若不等式
,
的解集构成的各区间的长度和超过
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3804eaa99063c55832b30824adaaa19e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eda48853e8bdb7e266370b4e0d5a258.png)
(1)若函数的定义域为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dd780a31d5cec6f5f1e8375821f8783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff00f543f40e9e87b2447f43813a9229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)在(1)的条件下,定义区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b133403156e1275c9fefff08b49dcfbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320cba4d29e050a7e9f4e3b24bdbbc86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/430f2f0dd785bf1ccaeb6134635e09a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8d309a6b38062e4d0bc845115ca56d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1163c658debbc7058e1e5d6d121da8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/412b61b3ea2f684925b14e78efae8a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a347ddcef71106c6fd64d3b0edd3b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58633cdffbb485e0f28daf965e06fcbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdab625e32e38d1c72c901cece0e147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
您最近一年使用:0次
2016-12-04更新
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232次组卷
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2卷引用:2015-2016学年福建上杭一中高一下期末模拟二数学试卷