diff --git a/工具v2/文本文件/metadata.txt b/工具v2/文本文件/metadata.txt index c171db91..77202b0d 100644 --- a/工具v2/文本文件/metadata.txt +++ b/工具v2/文本文件/metadata.txt @@ -1,22 +1,298 @@ -remark +ans -021552 -(20240307, 主要错因) 没写清楚具体角度所在范围以及三角比符号的判断过程; 计算错误 +024622 +$[2,3]$ -021557 -(20240307, 主要错因) 没写清楚具体角度所在范围以及三角比符号的判断过程; 计算错误 +024623 +$[2,+\infty)$ -021566 -(20240307, 主要错因) 未说明两个角的正切的乘积不能为$1$ +024624 +$[0,+\infty)$ -021570 -(20240308, 主要错因) (2)未能根据三角比找到正确的角; 未能根据角的范围找到正确的角 +024625 +$x=a$或$x=b$ -021571 -(20240308, 主要错因) 未能将式子化简为题目要求的形式 +024626 +$6$ -021572 -(20240308, 主要错因) 未能根据三角比找到正确的角 +024627 +$[2,+\infty)$ + +024628 +$\mathbf{R}$ + +024629 +$0$ + +024630 +$(-\infty,1)$ + +024631 +$B\subset A$ + +024632 +A + +024633 +A + +024634 +D + +024635 +D + +024636 +$10$ + +024637 +(1) $x=2$, $y=-1$; (2) $\overline{A \cap B}=\{-3,-2,0,1,2\}$, $\overline{A \cup B}=\{-3,0,1\}$ + +024638 +(1) $(1,2]\cup [3,+\infty)$ + +024639 +(1) $(-\dfrac{1}{3},1)$; (2) $(-\infty,-\dfrac{1}{2}]\cup [\dfrac{3}{2},+\infty)$ + +024640 +(1) $(-3,3]$; (2) $[3,+\infty)$ + +024641 +$<$ + +024642 +$(-\dfrac{1}{7},\dfrac{1}{5})$ + +024643 +必要非充分 + +024644 +$[3,+\infty)$ + +024645 +$[-\dfrac{3}{2},3)$ + +024646 +$\{11,12,14,15\}$ + +024647 +$-4$ + +024648 +$-1$ + +024649 +$[7,8]$ + +024650 +\textcircled{3}\textcircled{5} + +024651 +D + +024652 +C + +024653 +D + +024654 +A + +024655 +$[-\dfrac{1}{2}, 0)\cup (0,+\infty)$ + +024656 +$[\dfrac{1}{2},2]$ + +024657 +恒成立, 证明略 + +024658 +高为$88\text{cm}$, 宽为$55\text{cm}$ + +024659 +(1) $(\infty,-2)\cup (2,+\infty)$; (2) 证明略 + +024660 +$\dfrac{8}{5}$ + +024661 +$-9a$ + +024662 +$2+\dfrac{3\sqrt{2}}{2}$ + +024663 +$12$ + +024664 +$\dfrac{5a-3b+3}{2}$ + +024665 +$4$ + +024666 +$10$ + +024667 +$7\sqrt{2}$ + +024668 +$0$或$1$ + +024669 +$1$ + +024670 +B + +024671 +D + +024672 +B + +024673 +D + +024674 +(1) $8$; (2) $3$; (3) $21\sqrt{5}$ + +024675 +$a=6$, $b=8$, $c=10$ + +024676 +$-4$ + +024677 +最大值为$0$, 最小值为$-1$ + +024678 +$0$ + +024679 +$y=x^3$ + +024680 +$(-\infty,0)\cup (\dfrac{1}{3},+\infty)$ + +024681 +$(0,+\infty)$ + +024682 +$\dfrac{1}{2}$ + +024683 +$1$ + +024684 +$(-4,-1)\cup (4,+\infty)$ + +024685 +$(-\infty,-1]\cup [3,+\infty)$ + +024686 +$(0,1)$ + +024687 +$(-1,-\dfrac{1}{2}$ + +024688 +$(0,\dfrac{1}{4}]$ + +024689 +C + +024690 +C + +024691 +D + +024692 +A + +024693 +$1,3,5$或$7$ + +024694 +$(-\infty,-1)\cup (0,+\infty)$ + +024695 +(1) $3$年; (2) 按第二种方式能获得更多的利息, 利息差约为$1139.11$元 + +024696 +$(-\infty,-8]$ + +024697 +最大值为$2$, 最小值为$0$ + +024698 +$\dfrac{1-x}{1+x}$ + +024699 +偶 + +024700 +$1$ + +024701 +$x^2-2$ + +024702 +$[-1,+\infty)$ + +024703 +$2\sqrt{2}$ + +024704 +$[1,4]$ + +024705 +$[-4,-\dfrac{3}{2}]$ + +024706 +$\dfrac{27}{2}$ + +024707 +$[\dfrac{1}{2},1)\cup [3,+\infty)$ + +024708 +A + +024709 +D + +024710 +B + +024711 +C + +024712 +(1) $g(m)=-(m-\dfrac{1}{2})^2-\dfrac{3}{4}$; (2) 最大值为$-\dfrac{3}{4}$, 最小值为$-3$ + +024713 +(1) 在$(0,\sqrt{3}]$上严格减, 在$[\sqrt{3},+\infty)$上严格增, 大致图像如下: \begin{center} +\begin{tikzpicture}[>=latex, scale = 0.3] +\draw [->] (0,0) -- (8,0) node [below] {$x$}; +\draw [->] (0,0) -- (0,{8+3/8}) node [left] {$y$}; +\draw (0,0) node [below left] {$O$}; +\draw [domain = {3/8}:8, samples = 100] plot (\x,{\x+3/\x}); +\end{tikzpicture} +\end{center} +(2) 当$04$时, 最小值为$2+\dfrac{a}{2}$ + +024714 +(1) $g(x)=-x^2+2x$; (2) $(-\infty,0]$ + +024715 +(1) $f(x)=\begin{cases}\dfrac{1}{x^2+1}, & x>0, \\ 0, & x=0, \\ -\dfrac{1}{x^2+1}, & x<0;\end{cases}$ (2) $(-1,1)$ + +024716 +(1) $p(t)=\begin{cases}-2t^2+40t+200, & 2\le t<10, \\ 400, & 10\le t\le 20,\end{cases}$ 发车间隔为$8$分钟时, 电车的载客量为$392$人; (2) 发车间隔为$5$分钟时, 该线路每分钟的收益最大 + +024717 +(1) 都是``均分函数'', 理由略; (2) $[\dfrac{1}{9},+\infty)$; (3) $[\dfrac{1}{3},\dfrac{7}{3}]$ -018390 -(20240308, 主要错因) 计算错误(不能合理分步骤求解, 直接展开导致式子复杂, 计算出错; 三角比值和和差展开公式符号出错); 顺时针和逆时针旋转加减角度判断错误 \ No newline at end of file diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 627cb825..8dd465d4 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -681149,7 +681149,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[2,3]$", "solution": "", "duration": -1, "usages": [], @@ -681171,7 +681171,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[2,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -681193,7 +681193,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[0,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -681216,7 +681216,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$x=a$或$x=b$", "solution": "", "duration": -1, "usages": [], @@ -681238,7 +681238,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$6$", "solution": "", "duration": -1, "usages": [], @@ -681258,7 +681258,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[2,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -681282,7 +681282,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\mathbf{R}$", "solution": "", "duration": -1, "usages": [], @@ -681304,7 +681304,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [], @@ -681329,7 +681329,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,1)$", "solution": "", "duration": -1, "usages": [], @@ -681349,7 +681349,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$B\\subset A$", "solution": "", "duration": -1, "usages": [], @@ -681371,7 +681371,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -681393,7 +681393,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -681415,7 +681415,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -681435,7 +681435,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -681458,7 +681458,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$10$", "solution": "", "duration": -1, "usages": [], @@ -681478,7 +681478,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $x=2$, $y=-1$; (2) $\\overline{A \\cap B}=\\{-3,-2,0,1,2\\}$, $\\overline{A \\cup B}=\\{-3,0,1\\}$", "solution": "", "duration": -1, "usages": [], @@ -681499,7 +681499,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $(1,2]\\cup [3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -681519,7 +681519,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $(-\\dfrac{1}{3},1)$; (2) $(-\\infty,-\\dfrac{1}{2}]\\cup [\\dfrac{3}{2},+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -681539,7 +681539,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $(-3,3]$; (2) $[3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -681559,7 +681559,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$<$", "solution": "", "duration": -1, "usages": [], @@ -681579,7 +681579,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(-\\dfrac{1}{7},\\dfrac{1}{5})$", "solution": "", "duration": -1, "usages": [], @@ -681601,7 +681601,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "必要非充分", "solution": "", "duration": -1, "usages": [], @@ -681621,7 +681621,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -681641,7 +681641,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[-\\dfrac{3}{2},3)$", "solution": "", "duration": -1, "usages": [], @@ -681663,7 +681663,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\{11,12,14,15\\}$", "solution": "", "duration": -1, "usages": [], @@ -681683,7 +681683,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-4$", "solution": "", "duration": -1, "usages": [], @@ -681705,7 +681705,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-1$", "solution": "", "duration": -1, "usages": [], @@ -681730,7 +681730,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[7,8]$", "solution": "", "duration": -1, "usages": [], @@ -681753,7 +681753,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "\\textcircled{3}\\textcircled{5}", "solution": "", "duration": -1, "usages": [], @@ -681777,7 +681777,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -681797,7 +681797,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -681817,7 +681817,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -681843,7 +681843,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -681863,7 +681863,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$[-\\dfrac{1}{2}, 0)\\cup (0,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -681883,7 +681883,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$[\\dfrac{1}{2},2]$", "solution": "", "duration": -1, "usages": [], @@ -681903,7 +681903,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "恒成立, 证明略", "solution": "", "duration": -1, "usages": [], @@ -681923,7 +681923,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "高为$88\\text{cm}$, 宽为$55\\text{cm}$", "solution": "", "duration": -1, "usages": [], @@ -681943,7 +681943,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $(\\infty,-2)\\cup (2,+\\infty)$; (2) 证明略", "solution": "", "duration": -1, "usages": [], @@ -681966,7 +681966,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{8}{5}$", "solution": "", "duration": -1, "usages": [], @@ -681988,7 +681988,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$-9a$", "solution": "", "duration": -1, "usages": [], @@ -682012,7 +682012,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2+\\dfrac{3\\sqrt{2}}{2}$", "solution": "", "duration": -1, "usages": [], @@ -682032,7 +682032,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$12$", "solution": "", "duration": -1, "usages": [], @@ -682052,7 +682052,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{5a-3b+3}{2}$", "solution": "", "duration": -1, "usages": [], @@ -682074,7 +682074,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$4$", "solution": "", "duration": -1, "usages": [], @@ -682098,7 +682098,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$10$", "solution": "", "duration": -1, "usages": [], @@ -682120,7 +682120,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$7\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -682145,7 +682145,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$0$或$1$", "solution": "", "duration": -1, "usages": [], @@ -682167,7 +682167,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -682189,7 +682189,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -682209,7 +682209,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -682229,7 +682229,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -682251,7 +682251,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -682272,7 +682272,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $8$; (2) $3$; (3) $21\\sqrt{5}$", "solution": "", "duration": -1, "usages": [], @@ -682292,7 +682292,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$a=6$, $b=8$, $c=10$", "solution": "", "duration": -1, "usages": [], @@ -682312,7 +682312,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$-4$", "solution": "", "duration": -1, "usages": [], @@ -682334,7 +682334,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "最大值为$0$, 最小值为$-1$", "solution": "", "duration": -1, "usages": [], @@ -682358,7 +682358,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$0$", "solution": "", "duration": -1, "usages": [], @@ -682378,7 +682378,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$y=x^3$", "solution": "", "duration": -1, "usages": [], @@ -682398,7 +682398,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,0)\\cup (\\dfrac{1}{3},+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -682420,7 +682420,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(0,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -682443,7 +682443,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{1}{2}$", "solution": "", "duration": -1, "usages": [], @@ -682463,7 +682463,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -682486,7 +682486,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(-4,-1)\\cup (4,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -682506,7 +682506,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(-\\infty,-1]\\cup [3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -682529,7 +682529,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(0,1)$", "solution": "", "duration": -1, "usages": [], @@ -682551,7 +682551,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(-1,-\\dfrac{1}{2}$", "solution": "", "duration": -1, "usages": [], @@ -682575,7 +682575,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$(0,\\dfrac{1}{4}]$", "solution": "", "duration": -1, "usages": [], @@ -682599,7 +682599,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -682619,7 +682619,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -682642,7 +682642,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -682662,7 +682662,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -682682,7 +682682,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$1,3,5$或$7$", "solution": "", "duration": -1, "usages": [], @@ -682705,7 +682705,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,-1)\\cup (0,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -682727,7 +682727,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $3$年; (2) 按第二种方式能获得更多的利息, 利息差约为$1139.11$元", "solution": "", "duration": -1, "usages": [], @@ -682747,7 +682747,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "$(-\\infty,-8]$", "solution": "", "duration": -1, "usages": [], @@ -682770,7 +682770,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "最大值为$2$, 最小值为$0$", "solution": "", "duration": -1, "usages": [], @@ -682794,7 +682794,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{1-x}{1+x}$", "solution": "", "duration": -1, "usages": [], @@ -682814,7 +682814,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "偶", "solution": "", "duration": -1, "usages": [], @@ -682837,7 +682837,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$1$", "solution": "", "duration": -1, "usages": [], @@ -682860,7 +682860,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$x^2-2$", "solution": "", "duration": -1, "usages": [], @@ -682882,7 +682882,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[-1,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -682905,7 +682905,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$2\\sqrt{2}$", "solution": "", "duration": -1, "usages": [], @@ -682927,7 +682927,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[1,4]$", "solution": "", "duration": -1, "usages": [], @@ -682947,7 +682947,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[-4,-\\dfrac{3}{2}]$", "solution": "", "duration": -1, "usages": [], @@ -682967,7 +682967,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$\\dfrac{27}{2}$", "solution": "", "duration": -1, "usages": [], @@ -682987,7 +682987,7 @@ "objs": [], "tags": [], "genre": "填空题", - "ans": "", + "ans": "$[\\dfrac{1}{2},1)\\cup [3,+\\infty)$", "solution": "", "duration": -1, "usages": [], @@ -683009,7 +683009,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "A", "solution": "", "duration": -1, "usages": [], @@ -683029,7 +683029,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "D", "solution": "", "duration": -1, "usages": [], @@ -683052,7 +683052,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "B", "solution": "", "duration": -1, "usages": [], @@ -683072,7 +683072,7 @@ "objs": [], "tags": [], "genre": "选择题", - "ans": "", + "ans": "C", "solution": "", "duration": -1, "usages": [], @@ -683092,7 +683092,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $g(m)=-(m-\\dfrac{1}{2})^2-\\dfrac{3}{4}$; (2) 最大值为$-\\dfrac{3}{4}$, 最小值为$-3$", "solution": "", "duration": -1, "usages": [], @@ -683112,7 +683112,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 在$(0,\\sqrt{3}]$上严格减, 在$[\\sqrt{3},+\\infty)$上严格增, 大致图像如下: \\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.3]\n\\draw [->] (0,0) -- (8,0) node [below] {$x$};\n\\draw [->] (0,0) -- (0,{8+3/8}) node [left] {$y$};\n\\draw (0,0) node [below left] {$O$};\n\\draw [domain = {3/8}:8, samples = 100] plot (\\x,{\\x+3/\\x});\n\\end{tikzpicture}\n\\end{center}\n(2) 当$04$时, 最小值为$2+\\dfrac{a}{2}$", "solution": "", "duration": -1, "usages": [], @@ -683132,7 +683132,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $g(x)=-x^2+2x$; (2) $(-\\infty,0]$", "solution": "", "duration": -1, "usages": [], @@ -683154,7 +683154,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $f(x)=\\begin{cases}\\dfrac{1}{x^2+1}, & x>0, \\\\ 0, & x=0, \\\\ -\\dfrac{1}{x^2+1}, & x<0;\\end{cases}$ (2) $(-1,1)$", "solution": "", "duration": -1, "usages": [], @@ -683174,7 +683174,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) $p(t)=\\begin{cases}-2t^2+40t+200, & 2\\le t<10, \\\\ 400, & 10\\le t\\le 20,\\end{cases}$ 发车间隔为$8$分钟时, 电车的载客量为$392$人; (2) 发车间隔为$5$分钟时, 该线路每分钟的收益最大", "solution": "", "duration": -1, "usages": [], @@ -683194,7 +683194,7 @@ "objs": [], "tags": [], "genre": "解答题", - "ans": "", + "ans": "(1) 都是``均分函数'', 理由略; (2) $[\\dfrac{1}{9},+\\infty)$; (3) $[\\dfrac{1}{3},\\dfrac{7}{3}]$", "solution": "", "duration": -1, "usages": [],