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1 . 若函数
是
上的偶函数,
是
上的奇函数,且满足
.
(1)求
,
的解析式;
(2)令
,证明函数
有且只有
个零点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74ea1f7cd5fd2d33bc2ff7e1866bfb1c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)令
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7863b54185da5a3f1a765e1aa0577e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
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7日内更新
|
226次组卷
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5卷引用:重庆市清华中学2022届高三上学期7月月考数学试题
重庆市清华中学2022届高三上学期7月月考数学试题福建省八县(市)一中2020-2021学年高二下学期期末联考数学试题福建省永泰县第一中学2020-2021学年高二下学期期末数学试题(已下线)专题07函数期末8种常考题型归类【好题汇编】-备战2023-2024学年高二数学下学期期末真题分类汇编(人教B版2019)(已下线)专题09 导数与零点、不等式综合常考题型归类--高二期末考点大串讲(人教B版2019选择性必修第三册)
2 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172f1df5c0e107cd16ea0fc22d528258.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() | D.![]() ![]() |
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3 . 设
,
,
则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c5748fb8d839ae50cdb0faf6adaf41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87bd9f5db8b97abf9bdd15b8efb6c64d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db65c5fa71af60d067f32e1a70774cd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知函数
是定义域为
的可导函数,若
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee0b94eef7875086f8aff56d4e1de81e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a1d88f08209350ff227f0f4ddba626b.png)
A.![]() | B.![]() |
C.![]() | D.![]() ![]() |
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解题方法
5 . 函数
的定义域是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df95f2230efaca4ac617849f60f24a1.png)
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解题方法
6 . 已知
,若对
使
成立,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef5a09ce49b6addb3e0091e37f4dccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6724baa4cfe8013e519545a4e6912eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032e8dc00cdc96860c9cbf8ac09677fc.png)
A.函数![]() |
B.当![]() ![]() ![]() |
C.实数![]() ![]() |
D.实数![]() ![]() |
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7 . 设,我们常用
来表示不超过
最大整数.如:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d959974d562cb9ef138676ae943bc19c.png)
(2)在锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38335830b93ac4d99c28a8e209eecb3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7f5573b30734d65648f61c0a94c98de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c9bcb51024df4a7d1a04e46ca12549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c6f4e9bb8b453665bfe9b8fa24711cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a1633c3dde29b96636a2300ab074f5.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48da06492a0b0c8a31a5dc1531e8f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47bb945c963b0d56df9d784d3e3288c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a9d89ec3d1181091ea159b40952b65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
8 . 已知函数
,
为实数,
的导函数为
,在同一直角坐标系中,
与
的大致图象不可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe94aea880c85dd0537d102306b001c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4b04824a308519a61318a82aa97a05.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-06-11更新
|
472次组卷
|
2卷引用:重庆市南开中学校2024届高三下学期第八次质量检测(5月模拟预测)数学试题
9 . 给出以下两个数学运算(符号)定义:
①若函数
,则
,其中
称为函数
的
次迭代.如:
.
②对于正整数
,若
被
除得的余数为
,则称
同余于
,记为
.如:
.
(1)若函数
,求
;
(2)设
是一个给定的正整数,函数
记集合
.
①证明:当
时,
;
②求
并猜想
.
①若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac36cc9de2d52fa81b310df3c137559f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bbc5dcd0b5d4e94cb92e52ca31f0cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b956f95d6cdcded732751d6d74c14cab.png)
②对于正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0ace40e2e209924905e48bf00df631f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8b539bc9386988afc25da70e13ae899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706057125d5d481d23b0319e10e2d936.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08e564833f8450a876460a6db43dad1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91f1470cecf7c4da36644e5244775bf.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b44a1741d645756e39740a0818412e75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208bd4b35f6be79500cdf5d8e433e449.png)
①证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b94f6525788e512dbc8121c49b46bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502416314c8c26f8442e639ea6a5db13.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3cfeacc29e6a61c5b3b4e439c0a91df.png)
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10 . 对于一元三次函数
(
)图象上任一点
,若
在点
处的切线与
的图象交于另一点
,则称
为
的“伴随割点”,关于“伴随割点”,下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19951f3364fb04433feed743bc37975d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20849c00c47cbdc43f18d53341b6c4e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.点![]() |
B.若点![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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