1 . 已知函数
对任意的
,都有
成立.给出下列结论:
①
;②
;③
;④
.
其中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ab4b75fa22deba7fcbcdcb31dd45b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1638740ba651b56d0c833fe93d9995e4.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51eb2613dda00677d447c986cac505bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b53134510d90d1c1b3d413e910ca11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c73a98c1b3504e09bfbe0db849b0d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5a099039a6d72307e90f3701bd5406.png)
其中所有正确结论的序号是
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2 . 若
则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca24341509c05e672999202f2df0ebaf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3卷引用:北京市石景山区2023-2024学年高一上学期期末考试数学试卷
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解题方法
3 . 比较大小:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef14233360e5034fec67d42c84bf097e.png)
__________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef14233360e5034fec67d42c84bf097e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfe51ced71596bd20858ed0f4a062d7.png)
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4 . 已知a,b都是正实数,
(1)试比较
与
的大小,并证明;
(2)当
时,求证:
.
(1)试比较
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe2b05214c8b22507f0c36b110593d0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5106dbdadcc154f73ee91501ae4d43ff.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5be97cd1c7111b654d87d8fbb63b6a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8a8d68c4616b1e49c6556509a6cf84.png)
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5 . 1859年,我国清朝数学家李善兰将“function”一词译成“函数”,并给出定义:“凡此变数中函彼变数,则此为彼之函数”.
①若
,则函数
是偶函数
②若定义在
上的函数
在区间
上单调递增,在区间
上单调递增,则函数
在
上是增函数
③函数
的定义域为
,
,若
在
上是增函数,在
上是减函数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c52007fc20a4e1697de1630adaf4855.png)
④对于任意的
,函数
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1d276fda331c356dbdf459930c71a2.png)
上面关于函数性质的说法正确的序号是__________ .(请写出所有正确答案的序号)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964d724333a06f8c56fec61f2cea69a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
②若定义在
![](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/5e58768fc0df02f60aa54d00fe063c52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ed2f490aac02631c2ed9e6b76354a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
③函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f030c36bb8786df88d401792062a4100.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dcee29fdf5ec1ebd5f00c494c3fcb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/834e7745a2aaf9a7a31ddfcb9dc251c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a62461b16d4a05da2cfdd0c9b79a9874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c52007fc20a4e1697de1630adaf4855.png)
④对于任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fd7af568e3d9f444beb0ff41426477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6201963fcdd54887f2af50518bd908a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1d276fda331c356dbdf459930c71a2.png)
上面关于函数性质的说法正确的序号是
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解题方法
6 . 设
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4360ce512aea78e001e81beaf19e1b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/013e1e0129041e8be7ca7ab25567ccd3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-10-17更新
|
420次组卷
|
3卷引用:北京市东直门中学2023-2024学年高一上学期期中考试数学试卷
解题方法
7 . 已知函数
,
.无理数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)求证:
为奇函数;
(2)计算
的值;
(3)求证:R不是
的单调区间;
(4)求函数
的最小值;
(5)指数函数
是否可以表示成一个奇函数与一个偶函数的和的形式,若可以,直接写出你的结论,若不可以,请说明理由;
(6)已知
求证:
恒大于零.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e755e25eaafdc12a2d6aa6d3178cf4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3b8f0a0cb7d7a8e732c33a62fdfacf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11204e2fb6e560bf7a4ca26eaebfc526.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e755e25eaafdc12a2d6aa6d3178cf4b.png)
(2)计算
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f7a0971ccb6c1aeab5486bb4d8cc6a.png)
(3)求证:R不是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3b8f0a0cb7d7a8e732c33a62fdfacf.png)
(4)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3b8f0a0cb7d7a8e732c33a62fdfacf.png)
(5)指数函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
(6)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267a5770b8362cd8aa9bb573cf68633d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46be55c8f2760d6db125f46691a3de48.png)
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解题方法
8 . 已知函数
,则下列命题正确的有______ .(写出所有正确命题的编号)
①对于任意
,
,都有
成立;
②对于任意
,
,且
,都有
成立
③对于任意
,
,且
,都有
成立;
④存在实数
,使得对于任意实数
,都有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246de316aacce5e2a1b482840ff02f82.png)
①对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bf60c5e8996d138198fe74f30ce520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4e9b0e8693d64d9a59287e4802c535a.png)
②对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bf60c5e8996d138198fe74f30ce520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a1ead3649f31edf06d49f015dd7ece3.png)
③对于任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1bf60c5e8996d138198fe74f30ce520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deb572cf70a40f65fb90f3e93cdc439b.png)
④存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef96e6e80e958f6ae218594d4aa2f8b9.png)
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9 . 下列叙述中正确的是( )
A.若![]() ![]() ![]() ![]() |
B.函数![]() |
C.命题“![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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10 . 下列结论正确的是( )
A.当![]() ![]() | B.当![]() ![]() ![]() |
C.当![]() ![]() | D.当![]() ![]() |
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2022-11-15更新
|
903次组卷
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4卷引用:北京市丰台区第十二中学2022-2023学年高一上学期期中数学试题
北京市丰台区第十二中学2022-2023学年高一上学期期中数学试题(已下线)2.2 基本不等式精讲-【题型分类归纳】广东省潮州市饶平县第二中学2023-2024学年高一上学期期中考试数学试卷(已下线)FHsx1225yl011