From d5d3858cc12299660a6d9e9fac326f0e19e54f66 Mon Sep 17 00:00:00 2001 From: wangweiye7840 Date: Wed, 24 Jan 2024 16:16:37 +0800 Subject: [PATCH] =?UTF-8?q?=E6=94=B6=E5=BD=958=E9=A2=9824=E5=B1=8A?= =?UTF-8?q?=E5=AF=92=E5=81=87=E4=BD=9C=E4=B8=9A=E9=A2=98=E7=9B=AE?= 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 | 160 +++++++++++++++++++++++++++++++ 2 files changed, 163 insertions(+) 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 f5d2b165..cc23060f 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 @@ -1,3 +1,6 @@ 20240124-092236 023638:023648,010830,023649 +20240124-161545 +023652:023659 + diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index d1700528..a68a753c 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -639236,6 +639236,166 @@ "space": "4em", "unrelated": [] }, + "023652": { + "id": "023652", + "content": "下列求导运算中正确的是\\bracket{20}.\n\\fourch{$(\\ln 2)'=0$}{$(\\cos x)'=\\sin x$}{$(\\mathrm{e}^{-x})'=\\mathrm{e}^{-x}$}{$(\\dfrac{1}{x^5})'=-\\dfrac{1}{5}x^{-6}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023653": { + "id": "023653", + "content": "若函数 $f(x)=\\cos x+\\sin x$, 则 $f'(\\dfrac{\\pi}{4})=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023654": { + "id": "023654", + "content": "已知函数 $f(x)=a x^3+3 x^2+2$, 若 $f'(-1)=4$, 则 $a$ 的值等于\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023655": { + "id": "023655", + "content": "若函数 $f(x)=\\mathrm{e}^x \\ln x$, $f'(x)$ 为 $f(x)$ 的导函数, 则 $f'(1)$ 的值为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023656": { + "id": "023656", + "content": "若函数 $f(x)=x^4-2 x^3$, 则曲线 $y=f(x)$ 在点 $(1, f(1))$ 处的切线方程为\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023657": { + "id": "023657", + "content": "若函数 $f(x)=x^3-f'(1) x^2+2$, 则 $f(2)=$\\blank{50}.", + "objs": [], + "tags": [], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023658": { + "id": "023658", + "content": "已知函数 $f(x)=\\mathrm{e}^{-x}(\\sin x+\\cos x)$, 记 $f'(x)$ 是 $f(x)$ 的导函数, 若满足 $f'(x)=0$ 的所有正数 $x$ 从小到大排成数列 $\\{x_n\\}, n \\in \\mathbf{N}$, $n \\geq 1$, 则数列 $\\{f(x_n)\\}$ 的通项公式是\\bracket{20}.\n\\fourch{$(-1)^n \\mathrm{e}^{-(n+1) \\pi}$}{$(-1)^{n+1}\\mathrm{e}^{-n \\pi}$}{$(-1)^n \\mathrm{e}^{-n \\pi}$}{$(-1)^{n+1}\\mathrm{e}^{-(n+1) \\pi}$}", + "objs": [], + "tags": [], + "genre": "选择题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [], + "remark": "", + "space": "", + "unrelated": [] + }, + "023659": { + "id": "023659", + "content": "已知 $f(x)=x \\ln x+x^2-x+2$, 曲线 $y=f(x)$ 在点 $(x_0, f(x_0))$($x_0>0$) 处的切线恰好经过坐标原点, 求 $x_0$ 的值.", + "objs": [], + "tags": [], + "genre": "解答题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "自拟题目", + "edit": [ + "20240124\t毛培菁" + ], + "same": [], + "related": [], + "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