名校
1 . 设全集为
,定义域为
的函数
是关于x的函数“函数组”,当n取
中不同的数值时可以得到不同的函数.例如:定义域为
的函数
,当
时,有
若存在非空集合
满足当且仅当
时,函数
在
上存在零点,则称
是
上的“跳跃函数”.
(1)设
,若函数
是
上的“跳跃函数”,求集合
;
(2)设
,若不存在集合
使
为
上的“跳跃函数”,求所有满足条件的集合
的并集;
(3)设
,
为
上的“跳跃函数”,
.已知
,且对任意正整数n,均有
.
(i)证明:
;
(ii)求实数
的最大值,使得对于任意
,均有
的零点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2425552313d50a253bfb3cb4e9974ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a43b2faa4f81f32d94612dce724e772b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5182856db60fa5cfda34c97b5748197a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02670179163cffe5070d209066b7aa12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d18ae300954e363c2637120f4f3ef82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45020afb5156159ad42add5537797ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05f8bcb38a5c47e2e8fe9889717fc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e77ed55488688257efc354fad8875c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c853fd24a33bd11fbf2d5dba50806d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00108abe0b3ee27e7549f6cc0d86c36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b52b4f24969673c863b5aff4fb6751ce.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02670179163cffe5070d209066b7aa12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3946552f0f9f048a916879402e4d315a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47efc68941a3be03f5bebbabfbe388fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e94f0ab8e7418164e0c7481150e6b5.png)
(i)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d80a81e375bf3c3bdc3603ef7a2a37.png)
(ii)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b05f8bcb38a5c47e2e8fe9889717fc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61b4ceef651d43872a078d48092417d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9fbab6e1a7963d26e1265e1686cba40.png)
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名校
解题方法
2 . 若实数
满足
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905487a2a54ec22ac51e56de4fe76c26.png)
A.![]() ![]() | B.![]() |
C.![]() ![]() | D.![]() |
您最近一年使用:0次
2024-02-21更新
|
857次组卷
|
3卷引用:专题6 学科素养与综合问题(多选题11)
名校
3 . 设函数
且
表示不超过实数
的最大整数,则函数
的值域是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50feaef0c83d6e46b5ba77688bb838d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755ea37c1ebdbdc49b92196b129e8b38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aea51d290a3460f405bb04a6e6c1a67.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
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4 . 已知集合
.给定一个函数
,定义集合
,若
对任意的
成立,则称该函数
具有性质“
”.给出下列函数:①
;②
;③
;④
其中具有性质“
”的函数的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e5d1aa4cc6d7420da507e3f32808d6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec0500974fa4ff5245dc7516e96410d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e847907fda445c04edd732d1b77acc88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e145b6046bc80d0ffecc61ac67c87ca1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f42b2a9736c8943106472a7398d2892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b629bea8e22de9bfc49158e2289871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
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解题方法
5 . 若函数
与
满足:对任意的
,总存在唯一的
,使
成立,则称
是
在区间
上的“
阶伴随函数”;当
时,则称
为区间
上的“
阶自伴函数”,
(1)判断
是否为区间
上的“2阶自伴函数”?并说明理由;
(2)若函数
为区间
上的“1阶自伴函数”,求
的值;
(3)若
是
在区间
上的“2阶伴随函数”,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37cb15d282a40c780c2b68287e47867e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28e384ba050b238e11f7c74d3002aab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41286a1ca05dc551a9f734e6ed89996f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd330acca8e17f5ff9aca1f0f312df50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9587df831df1af5e7dd6be5fdc7bd8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58547687c14a41680e0a429ae79c757d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ed4089763bb5e9c6cb838d6391a173.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970193f414f7f52993b9f6cbabb77a0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a8d6ad7aa09c9c5f552a4c8e867a6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697b5e0d89c89ea58ae14982046e86c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b6d3b74c1697e4efd1dd7181d2ea39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2023·广东广州·模拟预测
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解题方法
6 . 函数
是定义在R上的奇函数,当
时,
,则函数
在
上的所有零点之和为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b808a0c73d88d7ebe7ffeb023743e4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba8ae3e7d73cd70135e6e3d366b8672.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0656a62ca479cbc2ec613f9e88dc65c4.png)
A.-32 | B.32 | C.16 | D.8 |
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7 . 若函数
满足:对于任意正数s、t,都有
,
,
,则称函数
为“L函数”.
(1)试判断函数
是否是“L函数”;
(2)若函数
为“L函数”,求实数a的取值范围;
(3)若函数
为“L函数”,且
,求证:对任意
,都有
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bd6668744366fc80aa91e2c7853bbf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23624c379c76dcff423ada0c89083280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0035bf4d1cd0978e745d32536e78cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)试判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5222db87c8bf85e4548488f09e2d9dfc.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79e3cd8564b48c35ba4247b79fe3d9db.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d87cd4403487962c38c8707ba3ab3fa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1baf957b7b5f8ced7b6330c4f6d92290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e331b120141e088148a6e80b6376d3f2.png)
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解题方法
8 . 已知
,
是定义在
上的增函数,
,若对任意
,
,使得
成立,则称
是
在
上的“追逐函数”.已知
,则下列四个函数中是
在
上的“追逐函数”的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c98f2d5ac32d2fbf4d29cb34941b78f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aab23b08a206f2afb86a2d9109a26d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/208575de4f7422c995dd601c54d264d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6b462f8734a368277b55a5dc05382a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b405741480780f91e6342eaf76b16263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c98f2d5ac32d2fbf4d29cb34941b78f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b1c079afd1b058adc67a50f48f3d466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6d804ef44bfc64f824b0ccef71765e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-02-15更新
|
572次组卷
|
3卷引用:第四章 指数函数与对数函数(压轴题专练)-速记·巧练(人教A版2019必修第一册)
(已下线)第四章 指数函数与对数函数(压轴题专练)-速记·巧练(人教A版2019必修第一册)江苏省连云港市2022-2023学年高一上学期期末学业质量调研数学试题山西省朔州市怀仁市第一中学校2023-2024学年高一下学期第一次月考数学试题
名校
解题方法
9 . 设对于曲线
上任一点处的切线
,总存在曲线
上一点处的切线
,使得
,则实数a的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c9fb926fd11cf5f91c5d11eaa40f101.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b9bfa6d8385842f5cbd7c4a34e7c7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-05-15更新
|
1429次组卷
|
8卷引用:专题07 导数的概念及意义 (十一大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)
(已下线)专题07 导数的概念及意义 (十一大题型+过关检测专训)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)(已下线)专题10 切线问题【讲】江苏省苏州实验中学2021-2022学年高二下学期期中数学试题河南省周口市商水县实验高级中学2021-2022学年高二下学期第三次月考数学(理)试题贵州省三新改革联盟校2022-2023学年高二下学期5月联考数学试题(已下线)第02讲 函数的切线问题-【寒假预科讲义】2024年高二数学寒假精品课(人教A版2019)(已下线)高二下学期第一次月考选择题压轴题十四大题型专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第三册)陕西师范大学附属中学2023-2024学年高三第八次模考数学(理科)试题
名校
10 . 已知
,下列不等式,成立的一个是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-04-30更新
|
913次组卷
|
3卷引用:第三章 利用导数比较大小 专题一 同构具体函数比较大小 微点3 构造含三角函数的组合函数比较大小
(已下线)第三章 利用导数比较大小 专题一 同构具体函数比较大小 微点3 构造含三角函数的组合函数比较大小广东省广州市玉岩中学2021-2022学年高二下学期期中数学试题广东省中山市迪茵公学2021-2022学年高二下学期第三次月考数学试题