1 . 先解答(1)(2),再通过结果类比解答(3).
(1)求证:
;
(2)写出函数
的最小正周期;
(3)定义在
上的函数
满足
(其中
为非零常数),试猜想
是否为周期函数,并证明你的结论.
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870b39c0e1e837cee44a5eea25008384.png)
(2)写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457eb5e0000350b102d387a80cf3476b.png)
(3)定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4fd86f5e6a24e6caf07d4248c1e308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2 . 已知函数
的图象关于直线
对称.
(1)求证:函数
为奇函数.
(2)将
的图象向左平移
个单位,再将横坐标伸长为原来的
倍,得到
的图象,求
的单调递增区间.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d43b74b756db719479eefe6f9988f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de633b2c143b9f76b29cde1c6ffce71.png)
(1)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50f48e0f9a7bb20736f2a99940a6189.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50f48e0f9a7bb20736f2a99940a6189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d74c0570f3ef4fff3e0ba34204f8d70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
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2023-11-16更新
|
321次组卷
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2卷引用:山西省运城市2024届高三上学期期中数学试题
3 . 已知函数
.
(1)求函数
的定义域;
(2)求曲线
在点
处的切线方程;
(3)求证:当
时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554abe4a9038c2113c0401e4654c570b.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6faa9259567d80f5da69a5fc09e71658.png)
(3)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/031ed5002755bcdd53c26fd7ff27fa09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2608a57caffde627dbf140ca22a2ff8a.png)
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2020-06-15更新
|
680次组卷
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3卷引用:山西省运城市2022届高三上学期期中数学(理)试题
真题
名校
4 . 已知函数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11882a302c0a5e9f47833eb2416d0725.png)
(Ⅰ)求
的最小正周期和最小值;
(Ⅱ)已知
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11882a302c0a5e9f47833eb2416d0725.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(Ⅱ)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efbbc96fd62a9c2557c2f683c91eb3ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/126cc244e8b5a9cb557789613ba9d725.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4e7d4aa8b7a6719c0c1e2898930641.png)
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2019-01-30更新
|
1916次组卷
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6卷引用:2013-2014学年山西省吕梁学院附中高一下学期期中考试数学试卷
5 .
在平面直角坐标系中,
为坐标原点,
三点满足![](https://img.xkw.com/dksih/QBM/2011/3/25/1577382440157184/1577382441689088/STEM/0a6958787f2144f089c7ba99a356abab.png)
(Ⅰ)求证:
三点共线;
(Ⅱ)求
的值;
(Ⅲ)已知
、
,![](https://img.xkw.com/dksih/QBM/2011/3/25/1577382440157184/1577382441689088/STEM/fe1d4fd479b44799b1a6a159e9e59889.png)
的最小值为
,求实数
的值.
在平面直角坐标系中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edd51c782333e04862704165622ad68.png)
![](https://img.xkw.com/dksih/QBM/2011/3/25/1577382440157184/1577382441689088/STEM/0a6958787f2144f089c7ba99a356abab.png)
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edd51c782333e04862704165622ad68.png)
(Ⅱ)求
![](https://img.xkw.com/dksih/QBM/2011/3/25/1577382440157184/1577382441689088/STEM/5e31b8530a0043039506f0c5943e9d07.png)
(Ⅲ)已知
![](https://img.xkw.com/dksih/QBM/2011/3/25/1577382440157184/1577382441689088/STEM/98a5526591ea4a4d9216afab66036c31.png)
![](https://img.xkw.com/dksih/QBM/2011/3/25/1577382440157184/1577382441689088/STEM/268db6dfd9ce4fe4a6d280321692298a.png)
![](https://img.xkw.com/dksih/QBM/2011/3/25/1577382440157184/1577382441689088/STEM/fe1d4fd479b44799b1a6a159e9e59889.png)
![](https://img.xkw.com/dksih/QBM/2011/3/25/1577382440157184/1577382441689088/STEM/520d49af75914f11b6b6658be3df7827.png)
![](https://img.xkw.com/dksih/QBM/2011/3/25/1577382440157184/1577382441689088/STEM/d87b20b667bd4b7fb5c84b428c5284b3.png)
![](https://img.xkw.com/dksih/QBM/2011/3/25/1577382440157184/1577382441689088/STEM/6ca4037c922f49ab88be6eabc21e085f.png)
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