From 7b823586b1ce517a2c0a216d1164ef24f8a6f7e7 Mon Sep 17 00:00:00 2001 From: "weiye.wang" Date: Thu, 8 Dec 2022 22:44:24 +0800 Subject: [PATCH] 20221208 night --- 工具/寻找阶段末尾空闲题号.ipynb | 8 +- 工具/添加题目到数据库.ipynb | 14 +- 工具/识别题库中尚未标注的题目类型.ipynb | 50 +-- 文本处理工具/剪贴板文本整理_word文件.ipynb | 14 +- 题库0.3/Problems.json | 437 +++++++++++++++++++++ 5 files changed, 484 insertions(+), 39 deletions(-) diff --git a/工具/寻找阶段末尾空闲题号.ipynb b/工具/寻找阶段末尾空闲题号.ipynb index 59127149..db72de64 100644 --- a/工具/寻找阶段末尾空闲题号.ipynb +++ b/工具/寻找阶段末尾空闲题号.ipynb @@ -9,7 +9,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "首个空闲id: 12117 , 直至 020000\n", + "首个空闲id: 12138 , 直至 020000\n", "首个空闲id: 20227 , 直至 030000\n", "首个空闲id: 30496 , 直至 999999\n" ] @@ -45,7 +45,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -59,12 +59,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/添加题目到数据库.ipynb b/工具/添加题目到数据库.ipynb index 87f88ac2..81125659 100644 --- a/工具/添加题目到数据库.ipynb +++ b/工具/添加题目到数据库.ipynb @@ -7,10 +7,10 @@ "outputs": [], "source": [ "#修改起始id,出处,文件名\n", - "starting_id = 12117\n", - "origin = \"2021届杨浦区一模\"\n", - "filename = r\"C:\\Users\\Wang Weiye\\Documents\\wwy sync\\临时工作区\\自拟题目5.tex\"\n", - "editor = \"20221206\\t王伟叶\"" + "starting_id = 12138\n", + "origin = \"2011年春季高考\"\n", + "filename = r\"C:\\Users\\weiye\\Documents\\wwy sync\\临时工作区\\自拟题目4.tex\"\n", + "editor = \"20221208\\t王伟叶\"" ] }, { @@ -101,7 +101,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -115,12 +115,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/工具/识别题库中尚未标注的题目类型.ipynb b/工具/识别题库中尚未标注的题目类型.ipynb index 3d083fca..9bdbe041 100644 --- a/工具/识别题库中尚未标注的题目类型.ipynb +++ b/工具/识别题库中尚未标注的题目类型.ipynb @@ -9,27 +9,29 @@ "name": "stdout", "output_type": "stream", "text": [ - "012117 填空题\n", - "012118 填空题\n", - "012119 填空题\n", - "012120 填空题\n", - "012121 填空题\n", - "012122 填空题\n", - "012123 填空题\n", - "012124 填空题\n", - "012125 填空题\n", - "012126 填空题\n", - "012127 填空题\n", - "012128 填空题\n", - "012129 选择题\n", - "012130 选择题\n", - "012131 选择题\n", - "012132 选择题\n", - "012133 解答题\n", - "012134 解答题\n", - "012135 解答题\n", - "012136 解答题\n", - "012137 解答题\n" + "012138 填空题\n", + "012139 填空题\n", + "012140 填空题\n", + "012141 填空题\n", + "012142 填空题\n", + "012143 填空题\n", + "012144 填空题\n", + "012145 填空题\n", + "012146 填空题\n", + "012147 填空题\n", + "012148 填空题\n", + "012149 填空题\n", + "012150 填空题\n", + "012151 填空题\n", + "012152 选择题\n", + "012153 选择题\n", + "012154 选择题\n", + "012155 选择题\n", + "012156 解答题\n", + "012157 解答题\n", + "012158 解答题\n", + "012159 解答题\n", + "012160 解答题\n" ] } ], @@ -71,7 +73,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -85,12 +87,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/文本处理工具/剪贴板文本整理_word文件.ipynb b/文本处理工具/剪贴板文本整理_word文件.ipynb index 0d137649..e4332c17 100644 --- a/文本处理工具/剪贴板文本整理_word文件.ipynb +++ b/文本处理工具/剪贴板文本整理_word文件.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -464,6 +464,12 @@ "#以下是为\\log_瘦身\n", "modified_data = re.sub(r\"log[\\s]+_\",r\"log_\",modified_data)\n", "\n", + "#以下是mathpix之后的空格去除\n", + "for i in range(3):\n", + " modified_data = re.sub(r\"([\\u4e00-\\u9fa5])( )([\\u4e00-\\u9fa5])\",lambda x:x.group(1)+x.group(3),modified_data)\n", + " modified_data = re.sub(r\"\\$ \",\"$\",modified_data)\n", + " modified_data = re.sub(r\" \\$\",\"$\",modified_data)\n", + "\n", "setCopy(modified_data)\n", "\n", "with open(\"临时文件/outputfile.txt\",\"w\",encoding = \"utf8\") as f:\n", @@ -480,7 +486,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.9.7 ('base')", + "display_name": "Python 3.8.8 ('base')", "language": "python", "name": "python3" }, @@ -494,12 +500,12 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.7" + "version": "3.8.8" }, "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "e4cce46d6be9934fbd27f9ca0432556941ea5bdf741d4f4d64c6cd7f8dfa8fba" + "hash": "d311ffef239beb3b8f3764271728f3972d7b090c974f8e972fcdeedf230299ac" } } }, diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index dd2171c7..bee88d93 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -299605,6 +299605,443 @@ "remark": "", "space": "12ex" }, + "012138": { + "id": "012138", + "content": "函数$y=\\lg(x-2)$的定义域是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题1", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012139": { + "id": "012139", + "content": "若集合$A=\\{x | x \\ge 1\\}$, $B=\\{x | x^2 \\le 4\\}$, 则 $A \\cap B=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题2", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012140": { + "id": "012140", + "content": "在 $\\triangle ABC$ 中, 若 $\\tan A=\\dfrac{\\sqrt 2}3$, 则 $\\sin A=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题3", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012141": { + "id": "012141", + "content": "若行列式$\\begin{vmatrix}2^x & 4 \\\\1 & 2\\end{vmatrix}=0$, 则 $x=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题4", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012142": { + "id": "012142", + "content": "若 $\\sin x=\\dfrac 13$, $x \\in[-\\dfrac{\\pi}2, \\dfrac{\\pi}2]$, 则 $x=$\\blank{50}(结果用反三角函数表示).", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题5", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012143": { + "id": "012143", + "content": "$(x+\\dfrac 1x)^6$ 的二项展开式的常数项为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题6", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012144": { + "id": "012144", + "content": "两条直线 $l_1: x-\\sqrt 3 y+2=0$ 与 $l_2: x-y+2=0$夹角的大小是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题7", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012145": { + "id": "012145", + "content": "若$S_n$为等比数列$\\{a_n\\}$的前$n$项和, $8 a_2+a_5=0$, 则 $\\dfrac{S_6}{S_3}=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题8", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012146": { + "id": "012146", + "content": "若椭圆$C$的焦点和顶点分别是双曲线$\\dfrac{x^2}5-\\dfrac{y^2}4=1$的顶 点和焦点, 则椭圆$C$的方程是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题9", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012147": { + "id": "012147", + "content": "若点$O$和点$F$分别为椭圆$\\dfrac{x^2}2+y^2=1$的中心和左焦点, 点$P$为椭圆上的任意一点, 则$|OP|^2+|PF|^2$的最小值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题10", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012148": { + "id": "012148", + "content": "根据如图所示的程序框图, 输出结果$i=$\\blank{50}.(缺框图)", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题11", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012149": { + "id": "012149", + "content": "2011年上海春季高考有$8$所高校招生, 如果某$3$位同学恰好被其中$2$所高校录取, 那么录取方法的种数为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题12", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012150": { + "id": "012150", + "content": "有一种多面体的饰品, 其表面由$6$个正方形和$8$个正三角形组成(如图), $A B$与$CD$所成角的大小是\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, z = {(215:0.5)}]\n\\def\\l{2}\n\\draw (0,0,0) coordinate (A);\n\\draw (A) ++ (\\l,0,0) coordinate (B);\n\\draw (A) ++ (\\l,0,-\\l) coordinate (C);\n\\draw (A) ++ (0,0,-\\l) coordinate (D);\n\\draw (A) ++ (0,\\l,0) coordinate (A1);\n\\draw (B) ++ (0,\\l,0) coordinate (B1);\n\\draw (C) ++ (0,\\l,0) coordinate (C1);\n\\draw (D) ++ (0,\\l,0) coordinate (D1);\n\\draw ($(A)!0.5!(B)$) coordinate (M);\n\\draw ($(B)!0.5!(C)$) coordinate (N) node [right] {$D$};\n\\draw ($(C)!0.5!(D)$) coordinate (P);\n\\draw ($(D)!0.5!(A)$) coordinate (Q);\n\\draw (M) ++ (0,\\l) coordinate (M1);\n\\draw (N) ++ (0,\\l) coordinate (N1);\n\\draw (P) ++ (0,\\l) coordinate (P1) node [above] {$B$};\n\\draw (Q) ++ (0,\\l) coordinate (Q1) node [above] {$A$};\n\\draw ($(A)!0.5!(A1)$) coordinate (A2);\n\\draw ($(B)!0.5!(B1)$) coordinate (B2);\n\\draw ($(C)!0.5!(C1)$) coordinate (C2) node [right] {$C$};\n\\draw ($(D)!0.5!(D1)$) coordinate (D2);\n\\draw (M) -- (A2) -- (Q) -- cycle (M) -- (B2) -- (N) -- cycle;\n\\draw (N) -- (C2) -- (N1) -- (B2);\n\\draw (N1) -- (M1) -- (Q1) -- (P1) -- cycle;\n\\draw (B2) -- (M1) -- (A2);\n\\draw (A2) -- (Q1);\n\\draw [dashed] (C2) -- (P1) -- (D2) -- (P) -- cycle;\n\\draw [dashed] (N) -- (P) -- (Q);\n\\draw [dashed] (Q) -- (D2) -- (Q1);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题13", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012151": { + "id": "012151", + "content": "为求解方程$x^5-1=0$的虚根, 可以把原方程变形为 $(x-1)(x^4+x^3+x^2+x+1)=0$, 再变形为$(x-1)(x^2+a x+1)(x^2+b x+1)=0$, 由此可得原方程的一个虚根为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题14", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012152": { + "id": "012152", + "content": "若向量$\\overrightarrow a=(2,0)$, $\\overrightarrow b=(1,1)$ , 则下列结论正确的是\\bracket{20}.\n\\fourch{$\\overrightarrow a \\cdot \\overrightarrow b=1$}{$|\\overrightarrow a|=|\\overrightarrow b|$}{$(\\overrightarrow a-\\overrightarrow b) \\perp \\overrightarrow b$}{$\\overrightarrow a \\parallel \\overrightarrow b$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题15", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012153": { + "id": "012153", + "content": "函数 $f(x)=\\dfrac{4^x-1}{2^x}$ 的图像关于\\bracket{20}.\n\\fourch{原点对称}{直线$y=x$对称}{直线$y=-x$对称}{$y$轴对称}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题16", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012154": { + "id": "012154", + "content": "直线$l: y=k(x+\\dfrac 12)$与圆$C: x^2+y^2=1$的位置关系为\\bracket{20}.\n\\fourch{相交或相切}{相交或相离}{相切}{相交}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题17", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012155": { + "id": "012155", + "content": "若 $\\overrightarrow{a_1}$、$\\overrightarrow{a_2}$、$\\overrightarrow{a_3}$均为单位向量, 则$\\overrightarrow{a_1}=(\\dfrac{\\sqrt 3}3, \\dfrac{\\sqrt 6}3)$是$\\overrightarrow{a_1}+\\overrightarrow{a_2}+\\overrightarrow{a_3}=(\\sqrt 3, \\sqrt 6)$的\\bracket{20}.\n\\twoch{充分不必要条件}{必要不充分条件}{充分必要条件}{既不充分又不必要条件}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题18", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "" + }, + "012156": { + "id": "012156", + "content": "向量$\\overrightarrow a=(\\sin 2 x-1, \\cos x), \\overrightarrow b=(1,2 \\cos x)$, 设函数$f(x)=\\overrightarrow a \\cdot \\overrightarrow b$, 求函数$f(x)$的最小正周期及$x \\in[0, \\dfrac{\\pi}2]$时的最大值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题19", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012157": { + "id": "012157", + "content": "某甜品店制作一种蛋筒冰激凌, 上部分是半球形, 下半部分呈圆锥形(如图), 现把半径为$10\\text{cm}$ 的圆形蛋皮等分成$5$个扇形, 用一个蛋皮围成圆锥的侧面 (蛋皮厚度忽略不计), 求该蛋筒冰激凌的表面积和体积. (精确到$0.01$)\n\\begin{center}\n\\begin{tikzpicture}[>=latex,scale = 0.5]\n\\fill [gray!20] (0,{-2*sqrt(6)}) -- (1,0) arc (360:180:1 and 0.3) -- cycle;\n\\draw (0,{-2*sqrt(6)}) -- (1,0) (0,{-2*sqrt(6)}) -- (-1,0);\n\\draw (1,0) arc (360:180:1 and 0.3);\n\\draw [dashed] (1,0) arc (0:180:1 and 0.3);\n\\draw (1,0) arc (0:180:1);\n\\end{tikzpicture}\n\\end{center}", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题20", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012158": { + "id": "012158", + "content": "已知抛物线 $F:x^2=4y$.\\\\\n(1) $\\triangle ABC$ 的三个顶点在抛物线 $F$ 上, 记$\\triangle ABC$的三边 $AB$、$BC$、$CA$所在直线的斜率分别为$k_{AB}$、$k_{BC}$、$k_{CA}$, 若点 $A$在坐标原点, 求 $k_{AB}-k_{BC}+k_{CA}$的值;\\\\\n(2) 请你给出一个以$P(2,1)$为顶点, 且其余各顶点均为抛物线$F$上的动点的多边形, 写出多边形各边所在直线的斜率之间的关系式, 并说明理由. 说明: 第(2)题将根据结论的一般性程度给与不同的评分.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题21", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012159": { + "id": "012159", + "content": "定义域为 $\\mathbf{R}$, 且对任意实数 $x_1$、$x_2$都满足不等式$f(\\dfrac{x_1+x_2}2) \\le \\dfrac{f(x_1)+f(x_2)}2$的所有函数$f(x)$组成的集合记为$M$, 例如$f(x)=k x+b \\in M$.\\\\\n(1) 已知函数 $f(x)=\\begin{cases}x, & x \\ge 0,\\\\ \\dfrac 12 x & x<0,\\end{cases}$ 证明: $f(x) \\in M$;\\\\\n(2) 写出一个函数$f(x)$, 使得$f(x) \\not\\in M$, 并说明理由;\\\\\n(3) 写出一个函数$f(x) \\in M$, 使得数列极限$\\displaystyle\\lim_{n \\to \\infty} \\dfrac{f(n)}{n^2}=1$, $\\displaystyle\\lim_{n \\to \\infty} \\dfrac{f(-n)}{-n}=1$.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题22", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, + "012160": { + "id": "012160", + "content": "对于给定首项$x_0>\\sqrt[3]a(a>0)$, 由递推式$x_{n+1}=\\dfrac 12(x_n+\\sqrt {\\dfrac a{x_n}})$($n \\in \\mathbf{N}$, $n\\ge 1$)得到数列$\\{x_n\\}$, 且对于任意的$n \\in \\mathbf{N}$, $n\\ge 1$, 都有 $x_n>\\sqrt[3]a$, 用数列$\\{x_n\\}$可以计算$\\sqrt[3]a$的近似值.\\\\\n(1) 取$x_0=5$, $a=100$, 计算 $x_1$、$x_2$、$x_3$的值(精确到$0.01$), 并且归纳出$x_n$、$x_{n+1}$的大小关系;\\\\\n(2) 当$n \\ge 1$时, 证明: $x_n-x_{n+1}<\\dfrac 12(x_{n-1}-x_n)$;\\\\\n(3) 当$x_0 \\in [5,10]$时, 用数列$\\{x_n\\}$计算$\\sqrt [3]{100}$的近似值, 要求满足$|x_n-x_{n+1}|<10^{-4}$, 请你估计$n$, 并说明理由.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "2011年春季高考试题23", + "edit": [ + "20221208\t王伟叶" + ], + "same": [], + "related": [], + "remark": "", + "space": "12ex" + }, "020001": { "id": "020001", "content": "判断下列各组对象能否组成集合, 若能组成集合, 指出是有限集还是无限集.\\\\\n(1) 上海市控江中学$2022$年入学的全体高一年级新生;\\\\\n(2) 中国现有各省的名称;\\\\\n(3) 太阳、$2$、上海市;\\\\\n(4) 大于$10$且小于$15$的有理数;\\\\\n(5) 末位是$3$的自然数;\\\\\n(6) 影响力比较大的中国数学家;\\\\\n(7) 方程$x^2+x-3=0$的所有实数解;\\\\ \n(8) 函数$y=\\dfrac 1x$图像上所有的点;\\\\ \n(9) 在平面直角坐标系中, 到定点$(0, 0)$的距离等于$1$的所有点;\\\\\n(10) 不等式$3x-10<0$的所有正整数解;\\\\\n(11) 所有的平面四边形.",