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收录8题24届寒假作业题目

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wangweiye7840 2024-01-24 16:16:37 +08:00
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3
工具v2/文本文件/新题收录列表.txt
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20240124-092236
023638:023648,010830,023649
20240124-161545
023652:023659

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题库0.3/Problems.json
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"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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",