1 . 请仔细阅读以下材料:
已知
是定义在
上的单调递增函数.
求证:命题“设
,若
,则
”是真命题.
证明:因为
,由
得
.
又因为
是定义在
上的单调递增函数,
于是有
. ①
同理有
. ②
由①+ ②得
.
故,命题“设
,若
,则
”是真命题.
请针对以上阅读材料中的
,解答以下问题:
(1)试用命题的等价性证明:“设
,若
,则:
”是真命题;
(2)解关于
的不等式
(其中
).
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a141e697b1a31a9a4e759984e899a5.png)
求证:命题“设
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/b2a8db4930d64746bee7acb58118f1be.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/add4ea370e3946109d077624424d5f04.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/473303324fc54d9fbef44f60c383cdd4.png)
证明:因为
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/b2a8db4930d64746bee7acb58118f1be.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/add4ea370e3946109d077624424d5f04.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/8e1dba6af48b4f02a02353cfceac54bc.png)
又因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a141e697b1a31a9a4e759984e899a5.png)
于是有
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/e138ae2d9d174247aa79ca4be523361f.png)
同理有
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/6e01071f3f38469e8e15c3d76700b775.png)
由①+ ②得
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/473303324fc54d9fbef44f60c383cdd4.png)
故,命题“设
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/b2a8db4930d64746bee7acb58118f1be.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/add4ea370e3946109d077624424d5f04.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/473303324fc54d9fbef44f60c383cdd4.png)
请针对以上阅读材料中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)试用命题的等价性证明:“设
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/b2a8db4930d64746bee7acb58118f1be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36ce14a18f423fcff11def7512150e.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973809381376/1571973814910976/STEM/add4ea370e3946109d077624424d5f04.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d4c9d254df7fc5169fe8e745a3b74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5c0c6e3ada0970f9a1fefd7200ff677.png)
您最近一年使用:0次
2 . 请仔细阅读以下材料:
已知
是定义在
上的单调递增函数.
求证:命题“设
,若
,则
”是真命题.
证明 :因为
,由
得
.
又因为
是定义在
上的单调递增函数,
于是有
. ①
同理有
. ②
由①+ ②得
.
故,命题“设
,若
,则
”是真命题.
请针对以上阅读材料中的
,解答以下问题:
(1)试用命题的等价性证明:“设
,若
,则:
”是真命题;
(2)解关于
的不等式
(其中
).
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a141e697b1a31a9a4e759984e899a5.png)
求证:命题“设
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/24e4835206fe4a69b03e5c5562294155.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/8209882c950f4c02a7aa91c6ad4584ae.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/25072c5bb7274310b540c233b24508ed.png)
证明 :因为
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/24e4835206fe4a69b03e5c5562294155.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/8209882c950f4c02a7aa91c6ad4584ae.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/63e0cee9c0994ebe9e8c9162a5fd4c58.png)
又因为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a141e697b1a31a9a4e759984e899a5.png)
于是有
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/816123fe83654315b9ad464cbbd7d4fd.png)
同理有
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/4cb2879dd5224072a6253ea98f00a84c.png)
由①+ ②得
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/25072c5bb7274310b540c233b24508ed.png)
故,命题“设
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/24e4835206fe4a69b03e5c5562294155.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/8209882c950f4c02a7aa91c6ad4584ae.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/25072c5bb7274310b540c233b24508ed.png)
请针对以上阅读材料中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)试用命题的等价性证明:“设
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/24e4835206fe4a69b03e5c5562294155.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c36ce14a18f423fcff11def7512150e.png)
![](https://img.xkw.com/dksih/QBM/2015/1/28/1571973654781952/1571973660549120/STEM/8209882c950f4c02a7aa91c6ad4584ae.png)
(2)解关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d4c9d254df7fc5169fe8e745a3b74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eda48853e8bdb7e266370b4e0d5a258.png)
您最近一年使用:0次
3 . 给出下列结论:
①函数
在区间
上有且只有一个零点;
②已知l是直线,
是两个不同的平面.若
;
③已知
表示两条不同直线,
表示平面.若
;
④在
中,已知
,在求边c的长时有两解.其中所有正确结论的序号是:___________ .
①函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e05b19c6d1e9ba6c05a1cbbc49bfe3f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25e4511e421ad1196f51c51bae75f7e0.png)
②已知l是直线,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc14778010a33f90902ff17b1ec0ac73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9717a462a666730684dc12e9c37a410d.png)
③已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a46d5b2635e7f44e5e3b9a950c24130.png)
④在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbedc2cb6780d06422775668a3be2fcb.png)
您最近一年使用:0次
2015-02-12更新
|
666次组卷
|
3卷引用:2015届山东省莱州市高三上学期期末考试理科数学试卷