名校
解题方法
1 . 设
是由满足下列条件的函数
构成的集合:①方程
有实根;②
在定义域区间
上可导,且
满足
.
(1)判断
,
是否是集合
中的元素,并说明理由;
(2)设函数
为集合
中的任意一个元素,证明:对其定义域区间
中的任意
、
,都有
.
![](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/dd689fbacfbe6c1bd0953521bbf3638b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/724340d69477c0ec2418c392b22b1cab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8f3ed0020216a8fa9049e5e6962f51.png)
(1)判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ac66170eaf3901361af2d1a6426ec8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4921923069c4f38a0af1ff8637e35b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)设函数
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/572bd49cfabec7b34ec9f511e9e9c845.png)
您最近一年使用:0次
7日内更新
|
336次组卷
|
2卷引用:2024届广东省汕头市普通高考第二次模拟考试数学试题
名校
2 . 已知函数
(
).
(1)若
在
上的最小值为
,求a的值;
(2)证明:
存在唯一零点
且满足
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00bb85988077e4cc023328a5e0ba9b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7242b2ab643f9470da77e29d043b893.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c96f02f851f30177f6172b5f592149.png)
您最近一年使用:0次
名校
3 . 已知函数
.
(1)讨论函数
的单调性;
(2)若存在正数
,使
成立,求
的取值范围;
(3)若
,证明:对任意
,存在唯一的实数
,使得
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe008fe11acbc34a61c7f44c5811be57.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若存在正数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d41acc47493556617fe7b9e55093d10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9e6a220e85fa5a1d7c773bb143d46f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d701701514d29d22d56e8a35f797d267.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99851fb4df35dfb2c4efd4a839b901f.png)
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2024-04-18更新
|
1664次组卷
|
4卷引用:数学(广东专用02,新题型结构)
4 . 设函数
.
(1)讨论函数
的单调性;
(2)若
,讨论函数
的零点的个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98df4fa31d61157e294ef30130bb620.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e7693ec68924d30b448b3425c0803c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
您最近一年使用:0次
2024-04-16更新
|
692次组卷
|
2卷引用:2024届广东省高三毕业班综合能力测试(华娇教育摸底测试)数学试题
名校
5 . 已知函数
和
的定义域分别为
和
,若对任意
,恰好存在
个不同的实数
,使得
(其中
),则称
为
的“
重覆盖函数”.
(1)试判断
是否为
的“2重覆盖函数”?请说明理由;
(2)若
,为
,的“2重覆盖函数”,求实数
的取值范围;
(3)函数
表示不超过
的最大整数,如
.若
为
的“2024重覆盖函数”请直接写出正实数
的取值范围.
![](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/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c296e45b84cf67a98939aa7334e7d478.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3eddf991be37d25d033f78bd3511809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2d5df7922a4e98e8e07bf418dd48a7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe44a5aed663a9b61ef7355b38c77d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d1a18f254577a0ce74ceb27364b98.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/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b96b909824873058aebdaa54f6c21ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a264b8541eddc8ae86058de027d1a1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f246e5b05b68bb9fdeb12a319aa7136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa88c20e58953bba4ed04d3ce419df95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4f5908d6a1217e493ed7586b6964dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/240ca781ffd5d55cc9b7dd551879ce65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4987dca9120f6a58139fd3e412ed77c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a899e901b141a0a6d56e3387ecf9f047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2024-03-29更新
|
226次组卷
|
2卷引用:广东省广州市第六中学2023-2024学年高一下学期期中考试数学试题
名校
解题方法
6 . 已知函数
为奇函数.
(1)求a的值;
(2)设函数
,
i.证明:
有且只有一个零点;
ii.记函数
的零点为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b073296a8d31514d8b394331df70c2.png)
(1)求a的值;
(2)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b6625dd55e79c5115e6e7299cb83600.png)
i.证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
ii.记函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb2faa63899873813748f6a28b8a92e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be0b46f954f3590a00fe5a074e8e931b.png)
您最近一年使用:0次
2024-02-23更新
|
573次组卷
|
3卷引用:广东省广州市铁一中学2023-2024学年高一下学期3月月考数学试题
广东省广州市铁一中学2023-2024学年高一下学期3月月考数学试题浙江省温州市浙南名校联盟2023-2024学年高一下学期寒假返校联考数学试题(已下线)浙江省宁波市鄞州中学2023-2024学年高二下学期期中考试数学试题
7 . 已知函数
.
(1)当
时,不用计算器,用切线“以直代曲”,求
的近似值(精确到四位小数).
(2)讨论函数
的零点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ae859b52222aaf0b4d0950dba26e63.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd3a3849e7358307fe0f0102143e50e.png)
(2)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
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2024-02-17更新
|
416次组卷
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2卷引用:广东省汕头市潮阳实验学校2024届高三上学期第一次调研数学试题
8 . 如图,给出函数
的部分图象.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/b4ae34aa-0fdb-4eec-bca3-d295c8fafee1.png?resizew=161)
(1)请在图中同一坐标系内画出函数
的图象.设
与
在
轴左边的交点为
,试用二分法求出
的横坐标
的近似解(精确度为0.3);
(2)用
表示
,
中的较大者,记为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4ed159e3b82a2f8131c99117ee70e0.png)
,请写出
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/318a16f1950d06e5500c76d8f81a507f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/b4ae34aa-0fdb-4eec-bca3-d295c8fafee1.png?resizew=161)
(1)请在图中同一坐标系内画出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557eb194cf0abe382609f8e1325b4197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
(2)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531bcdb6324cb5a759301daddf9768c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4ed159e3b82a2f8131c99117ee70e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3682b41be6fbf083088212c1c6ffa7ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531bcdb6324cb5a759301daddf9768c0.png)
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9 . 已知函数
,不等式
解集为M,
(1)设函数
在
上存在零点,求实数m的取值范围;
(2)当
时,函数
(其中
)的最小值为
,求实数a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce427e97019745d570dd2728027fba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b65d53b1547f243d5a8ed642f8551dd.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b10664a63753466a594619215c4c16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfc595518cf752e1c7903dfff93dbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d6a28212810970ee8501118e1a1fc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1eaf48f1ad368af0b0961322e50d74e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
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10 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e5ff2705eb737adef9a6dc70559d79.png)
(1)已知
为单调递增函数,请判断
的单调性,并用单调性定义证明;
(2)若
,求证:方程
在区间
上有且仅有一个实数解.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b72eb501bf5451af98ab894176fb2a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e5ff2705eb737adef9a6dc70559d79.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b161347f6a2fcfd9bf0acf1e8a03fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b67287da8b741b449aa283c688fd080.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eaeb2ab68a49074d623ffca072fed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
您最近一年使用:0次