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修改18081题面的错误及19837答案的错误

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weiye.wang 2023-10-01 09:01:21 +08:00
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commit ec1d41ea08
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题库0.3/Problems.json
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@ -474325,21 +474325,22 @@
},
"018081": {
"id": "018081",
"content": "设$f(x)=\\ln x$, 函数$y=f(x)$的图像为$\\gama$. 作以下操作: 在$\\gama$上取点$A_1(a_1, f(a_1))$, 以$A_1$为切点作$\\gama$的切线交$y$轴于点$(0,a_2)$, 若$a_2>0$, 则在$\\gama$上取点$A_2(a_2,f(a_2))$, 以$A_2$为切点作$\\gama$的切线交$y$轴于点$(0,a_3)$,若$a_3>0$则依此下去……, 一旦$a_n\\leq 0(n\\geq 2)$则终止这一操作. 由此得到数列$\\{a_n\\}$.\\\\\n(1) 对于$\\{a_n\\}$中任意一项$a_m(m \\geq 2)$, 证明: $a_m=\\ln a_{m-1}-1$;\\\\\n(2) 对于$\\{a_n\\}$中任意一项$a_m(m \\geq 2)$, 比较$a_m$与$a_{m-1}-2$大小;\\\\\n(3) 是否存在$a_1$与正整数$k(k\\geq 3)$, 使得$\\{a_n\\}$的前$k$项$a_1, a_2 \\cdots a_k$依次成等差数列? 若存在, 求出$k$的所有可能取值; 若不存在, 说明理由.",
"content": "设$f(x)=\\ln x$, 函数$y=f(x)$的图像为$\\gamma$. 作以下操作: 在$\\gamma$上取点$A_1(a_1, f(a_1))$, 以$A_1$为切点作$\\gamma$的切线交$y$轴于点$(0,a_2)$, 若$a_2>0$, 则在$\\gamma$上取点$A_2(a_2,f(a_2))$, 以$A_2$为切点作$\\gamma$的切线交$y$轴于点$(0,a_3)$,若$a_3>0$则依此下去……, 一旦$a_n\\leq 0(n\\geq 2)$则终止这一操作. 由此得到数列$\\{a_n\\}$.\\\\\n(1) 对于$\\{a_n\\}$中任意一项$a_m(m \\geq 2)$, 证明: $a_m=\\ln a_{m-1}-1$;\\\\\n(2) 对于$\\{a_n\\}$中任意一项$a_m(m \\geq 2)$, 比较$a_m$与$a_{m-1}-2$大小;\\\\\n(3) 是否存在$a_1$与正整数$k(k\\geq 3)$, 使得$\\{a_n\\}$的前$k$项$a_1, a_2 \\cdots a_k$依次成等差数列? 若存在, 求出$k$的所有可能取值; 若不存在, 说明理由.",
"objs": [],
"tags": [
"第二单元",
"第四单元"
],
"genre": "解答题",
"ans": "(1)证明略;(2)$a_m\\le a_{m-1}-2$,当且仅当$a_{m-1}=1$时等号成立;(3)${3}$",
"ans": "(1)证明略;(2)$a_m\\le a_{m-1}-2$,当且仅当$a_{m-1}=1$时等号成立;(3)$\\{3\\}$",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2023年秋考试题21",
"edit": [
"20230608\t王伟叶",
"20230608\t王伟叶"
"20230608\t王伟叶",
"20231001\t王伟叶"
],
"same": [],
"related": [],
@ -513638,14 +513639,15 @@
"第一单元"
],
"genre": "4em",
"ans": "$",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "2025届高一校本作业必修第二章-20230918修改",
"edit": [
"20220901\t王伟叶\t伍杨超",
"20230918\t王伟叶"
"20230918\t王伟叶",
"20231001\t王伟叶"
],
"same": [],
"related": [