From 0d1d932c37b790f151f215e7801cd4431656574e Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Thu, 25 Jan 2024 12:54:20 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=95=E9=AB=98=E4=B8=89=E5=AF=92?= =?UTF-8?q?=E5=81=87=E4=BD=9C=E4=B8=9A47=E6=96=B0=E9=A2=98?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 工具v2/文本文件/新题收录列表.txt | 3 + 题库0.3/Problems.json | 166 ++++++++++++++++++++++++++++++- 2 files changed, 168 insertions(+), 1 deletion(-) diff --git a/工具v2/文本文件/新题收录列表.txt b/工具v2/文本文件/新题收录列表.txt index f6fe6496..27ee6207 100644 --- a/工具v2/文本文件/新题收录列表.txt +++ b/工具v2/文本文件/新题收录列表.txt @@ -139,3 +139,6 @@ 20240125-125210 023966:023969,000724,023970 +20240125-125411 +023971:023978 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 9ba3d2b7..8dbc253d 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -41883,7 +41883,9 @@ "20220625\t王伟叶" ], "same": [], - "related": [], + "related": [ + "023978" + ], "remark": "", "space": "4em", "unrelated": [] @@ -646095,6 +646097,168 @@ "space": "4em", "unrelated": [] }, + "023971": { + "id": "023971", + "content": "函数 $y=x^2+x+1$($x \\in \\mathbf{R}$) 的单调减区间是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023972": { + "id": "023972", + "content": "函数 $f(x)=(\\dfrac{1}{2})^x-\\log _3(x+2)$ 在区间 $[-1,1]$ 上的最大值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023973": { + "id": "023973", + "content": "若函数 $f(x)=\\dfrac{1}{x}$ 在区间 $[2, a]$ 上的最大值与最小值的和为 $\\dfrac{3}{4}$, 则实数 $a$ 的值等于\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023974": { + "id": "023974", + "content": "已知函数 $f(x)=\\begin{cases}x+4,& x0$) 在 $[3,+\\infty)$ 上是严格增函数, 则实数 $a$ 的取值范围是\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023977": { + "id": "023977", + "content": "已知函数 $f(x)=\\begin{cases}\\mathrm{e}^x,& x \\leq 0,\\\\\\ln x,& x>0,\\end{cases}$, $f(x)=f(x)+x+a$. 若 $g(x)$ 存在 $2$ 个零点, 则实数 $a$的取值范围是\\bracket{20}.\n\\fourch{$[-1,0)$}{$[0,+\\infty)$}{$[-1,+\\infty)$}{$[1,+\\infty)$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023978": { + "id": "023978", + "content": "已知函数 $f(x)=\\dfrac{x^2+2 x+a}{x}$, $x \\in[1,+\\infty)$.\\\\\n(1) 当 $a=\\dfrac{1}{2}$ 时, 用定义证明函数的单调性并求函数 $f(x)$ 的最小值;\\\\\n(2) 若对任意 $x \\in[1,+\\infty)$, $f(x)>0$ 恒成立, 试求实数 $a$ 的取值范围.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240125\t毛培菁" + ], + "same": [], + "related": [ + "001232" + ], + "remark": "", + "space": "4em", + "unrelated": [] + }, "030001": { "id": "030001", "content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0