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1 . 已知无穷数列
,
.性质
,
,;性质
,
,
,下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76aef4cdcb5af742ce28003b7b6c8c20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61afe83270a244e2af1995c9f4f51f72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8af17844e7059b9c96c75c8440671eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc5a0c2ef759ad38721f51ad2298c66e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0971a0dad04b09fab7c3f0eafe5b24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e7bd4fde43499209812ba20f87286c.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() |
D.若等比数列![]() ![]() |
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3卷引用:江西省南昌市第二中学2024届高三“九省联考”考后适应性测试数学试题(一)
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解题方法
2 . 若函数
在定义域内存在两个不同的数
,
,同时满足
,且
在点
,
处的切线斜率相同,则称
为“切合函数”.
(1)证明:
为“切合函数”;
(2)若
为“切合函数”(其中
为自然对数的底数),并设满足条件的两个数为
,
.
(ⅰ)求证:
;
(ⅱ)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.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/abf7c745cd02f4620a175cf00ec85e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24a2c53e3b0b1c08803e95419f909d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecaca8409b3f51d22667a14559c58ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d275fbb3ee5cd1177ca5a2ceecbbef0f.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe0de54dfc96a2291e8d5e56676eabc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fb46178ba0560d96bd3a05891505b95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/041a7c8fc017f596542c5e6ec7d1c40b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c20b8bd265b07dd90690ad4e349c6dc.png)
(ⅱ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84cde09c609543feedc2e0c11992b2bd.png)
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2024-01-03更新
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4卷引用:江西省赣州市南康中学2024届高三上学期新高考“七省联考”考前数学猜题卷(一)
江西省赣州市南康中学2024届高三上学期新高考“七省联考”考前数学猜题卷(一)重庆市南开中学校2024届高三上学期第五次质量检测数学试题重庆市沙坪坝区南开中学校2024届高三上学期第五次质量检测数学试题(已下线)微考点2-5 新高考新试卷结构19题压轴题新定义导数试题分类汇编
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解题方法
3 . 已知实数m,n满足
,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5d4b55b21e776a254f07f56fab5c958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c294fe813bfa5e8ef0c612c7d1d1a9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5卷引用:江西省赣州市南康中学2024届高三上学期新高考“七省联考”考前数学猜题卷(一)
江西省赣州市南康中学2024届高三上学期新高考“七省联考”考前数学猜题卷(一)河南省部分名校2023-2024学年高三上学期阶段性测试(三)(11月)数学试题江苏省扬州市扬州中学2024届新高考一卷数学模拟测试一(已下线)模块五 全真模拟篇 基础1 期末终极研习室(2023-2024学年第一学期)高三广东省佛山市第一中学2024届高三下学期开学预测数学试题(一)
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4 . 已知函数
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
.( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f304a19256eb0935d95c2adc48eb4bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f57b5a7c0283d2638c7b5a0baba4040.png)
A.若曲线![]() ![]() ![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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7卷引用:江西省宜春市上高中学2022-2023学年高二下学期5月期中考试数学试题
5 . 已知函数
.
(1)若
在
上单调递增,求实数a的取值范围;
(2)当
时.
(i)求证:函数
在
上单调递增;
(ii)设区间
(其中
),证明:存在实数
,使得函数
在区间I上总存在极值点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef290c72466c30bc20d7414418cfaee.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
(i)求证:函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1899b95e2442b6a08a5a134b36ed7c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7754cc9374c8193dadb6875fb8a3fefb.png)
(ii)设区间
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e07062bde69560336def001c925eb7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb9dfa7ecdfa37e643c51193a388836.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d8047f0a8bd0cf4e250cd0fe80093b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bbd86a6b6493a67696125835eea5f76.png)
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6 . 若直线
与两曲线
分别交于
两点,且曲线
在
点处的切线为
,曲线
在
点处的切线为
,则下列结论:
①
,使
;②当
时,
取得最小值;
③
的最小值为2;④
.
其中所有正确结论的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26c7605338f5766155296b13cf99147.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db192285632d1991b4ee7a003a52205.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d115cf2f2e63304d4f31946db866de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a93a52c2b943e4c70ace99ed802d2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a93a52c2b943e4c70ace99ed802d2b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14efb0184968017766c8f60cf6fc31a1.png)
其中所有正确结论的序号是( )
A.① | B.①②③ |
C.①②④ | D.①②③④ |
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2021-12-04更新
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6卷引用:江西省抚州市临川第一中学2021-2022高二12月月考数学(文)试题
江西省抚州市临川第一中学2021-2022高二12月月考数学(文)试题江西省宜春市上高二中2022届高三5月第十次月考数学(理)试题四川省宜宾市普通高中2022届高三上学期第一次诊断测试理科数学试题(已下线)专题3-5 超难压轴小题:导数和函数归类(2)-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)(已下线)第07讲 利用导数研究函数的单调性(核心考点讲与练)-2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)(已下线)专题08 导数与函数综合压轴(选填题)-2