1 . 已知函数,若
的最小正周期为
.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9590ce4b87b155d12b86575d5586d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7afbd154d5f993012b880e4e0c7f9821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291c25fc6a69d6d0ccfb8d839b9b4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
①求实数取值范围;
②若,求实数
的取值范围.
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解题方法
2 . 对于两个函数:
和
,
的最大值为M,若存在最小的正整数k,使得
恒成立,则称
是
的“k阶上界函数”.
(1)若
,
是
的“k阶上界函数”.求k的值;
(2)已知
,设
,
,
.
(i)求
的最小值和最大值;
(ii)求证:
是
的“2阶上界函数”.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1cfb60420ff7e72c1b9d64f69ae063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6afd1b3aeae1bd415dba90e50c001c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ffea0f7bb26c02be91008a3a992a27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5289677c3bf66194c475c4c44f4a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06f45220c23094a3d9ef53b54b89d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2bc8d66faac1a06acfec68e28086bf.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b89d55ca6a541bce15e141a7e38285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66f0ca536621ec8db02707ba65917029.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ff2689759a35f3a8030b02be7a22c3.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e49794721f5504dd828acf49be37ff42.png)
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2022-01-24更新
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2卷引用:重庆市巴蜀中学2021-2022学年高一上学期期末数学试题
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3 . 已知函数
.
(1)求
的单调递增区间;
(2)当
时,关于
的方程
恰有三个不同的实数根,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be28f2d051d647edaee7697dc82f5e83.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd863f4329de75462506c99463cc1488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3c9f814c640d3e196c01c3cb81723e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2020-07-23更新
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8卷引用:重庆市北山中学2020-2021学年高一上学期期末数学试题
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解题方法
4 . 对于函数
,
与常数
,若存在
使得
成立,则称函数
与
是“
靠近函数”.
(1)设函数
,
,判断
与
是否为“1靠近函数”,并说明理由;
(2)若函数
与
为“1靠近函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4166972dec0aa3e8694a44eeb941a08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea10ff765f87d9379cf875e8d425df23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e29815099a20aefdf055c71a347dbb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a2f0102d111a1e63ec471da49dbd50a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8b6894e8c345a035e89ec672503a01f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e03ad0c315806342d6cd732a0b91a3.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90ba0d6fefae76fcdd43507c4b07b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4bba0decfa88c92d9fd153aa2b84388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-02-14更新
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2卷引用:重庆市南开中学2017-2018学年高一上学期期末数学试题
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5 . 已知定义在
的奇函数
满足:①
;②对任意
均有
;③对任意
,均有
.
(1)求
的值;
(2)利用定义法证明
在
上单调递减;
(3)若对任意
,恒有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/528597e52afcd661e2aaca97e709ca29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ed85d47b4f488a9b5e211938cc5424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0aa2ef928b6e3341d0a0dc6d8055b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a71baf6217604517fd98fa97d0f55b43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28f616b1f56991ee75caae3ac35208b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d8f51aac18216cabd2b0082dca6090.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d55ef0d1b7ea88d92fd6e1ecebb5f5.png)
(2)利用定义法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a7a4a037a4dfe973f1eb683d93d799.png)
(3)若对任意
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf97da45123318474a22828c99d45d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4864f1ffd5317f2f89c90ffc91ece407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2020-01-30更新
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2卷引用:重庆市第一中学2019-2020学年高一上学期期末数学试题
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6 . 已知向量
,
,定义:
,其中
.若
,则
的值不可能 为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb58883caf5c8ca1e94389839d294b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbb10314fbe1a7b3a8af7da92158d42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9944600eafc9bf8c2e62bae49f62a345.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3ede869e508a8c8bda34a16782f863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9331761428603a9ab3ecdb1aaf331d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20126588f4128288dc0e0d1d84de632a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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