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收录24届高三寒假作业03新题

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wangweiye7840 2024-01-24 16:32:42 +08:00
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commit 1649b931b6
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3
工具v2/文本文件/新题收录列表.txt
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@ -7,3 +7,6 @@
20240124-162441
023660:023664,040325,023665
20240124-163155
023666:023673

182
题库0.3/Problems.json
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@ -49057,7 +49057,9 @@
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@ -410828,7 +410830,9 @@
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@ -639516,6 +639520,172 @@
"space": "4em",
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"023666": {
"id": "023666",
"content": "若 $a>0$, 函数 $f(x)=a^2 x-\\dfrac{1}{3}x^3$ 的极小值为 $-\\dfrac{4}{3}$, 则实数 $a$ 的值为\\blank{50}.",
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"20240124\t毛培菁"
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"023667": {
"id": "023667",
"content": "函数 $f(x)=6+12 x-x^3$ 在 $[-1,3]$ 上的最大值为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
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"023668": {
"id": "023668",
"content": "若函数 $f(x)=x^3+a x^2+3 x-9$ 在 $x=-3$ 时取得极值, 则实数 $a$ 等于\\blank{50}.",
"objs": [],
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"023669": {
"id": "023669",
"content": "函数 $f(x)=(1-x) \\mathrm{e}^x$ 的最大值为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
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"023670": {
"id": "023670",
"content": "若函数 $f(x)=\\mathrm{e}^x(-x^2+2 x+a)$ 在区间 $(a, a+1)$ 上存在最大值, 则实数 $a$ 的取值范围为\\blank{50}.",
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"023671": {
"id": "023671",
"content": "若函数 $f(x)=\\dfrac{1}{3}x^3+x^2-\\dfrac{2}{3}$ 在区间 $(a, a+3)$ 内既存在最大值也存在最小值, 则实数 $a$ 的取值范围是\\blank{50}.",
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"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
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"023672": {
"id": "023672",
"content": "若函数 $f(x)$ 的导函数 $f'(x)$ 的图像如图所示, 则下列结论中正确的序号是\\blank{50}.\\\\\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.5]\n\\draw [->] (-4,0) -- (7,0) node [below] {$x$};\n\\draw [->] (0,-3) -- (0,3) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\foreach \\i in {-3,-2,1,3,5,6}\n{\\draw (\\i,0.1) -- (\\i,0) node [below] {$\\i$};};\n\\draw (-1,0.1) -- (-1,0) node [above] {$-1$};\n\\draw (-3,-3) sin (-2,1) cos (-1,0) sin (0,-1) cos (1,0) sin (3,2) cos (4.5,0) sin (5,-0.5) cos (6,1.5);\n\\draw [dashed] (-2,0) -- (-2,1) (3,0) -- (3,2) (6,0) -- (6,1.5);\n\\end{tikzpicture}\n\\end{center}\n\\textcircled{1} 当 $x=1$ 时, 函数 $f(x)$ 取得极小值;\\\\\n\\textcircled{2} 函数 $f(x)$ 在区间 $(-1,1)$ 上是严格增函数;\\\\\n\\textcircled{3} 当 $x=3$ 时, 函数 $f(x)$ 取得极大值;\\\\\n\\textcircled{4} 函数 $f(x)$ 在区间 $(5,6)$ 上是严格增函数.",
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"040614"
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"023673": {
"id": "023673",
"content": "已知函数 $f(x)=-x^3+a x^2+b x+c$($a$、$b$、$c \\in \\mathbf{R}$), 且 $f'(-1)=f'(3)=0$.\\\\\n(1) 求 $a-b$ 的值;\\\\\n(2) 若函数 $f(x)$ 在 $[-2,2]$ 上的最大值为 $20$, 求函数 $f(x)$ 在 $[-1,4]$ 上的最小值.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
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"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.",
@ -706563,7 +706733,9 @@
"20230401\t王伟叶"
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@ -711154,7 +711326,9 @@
"20230423\t王伟叶"
],
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