收录高三寒假作业47新题

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
+

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 $f(x)=\\begin{cases}x+4,&  x<a\\\\x^2-2 x,&  x \\geq a,\\end{cases}$ 若函数 $f(x)$ 的值域为 $\\mathbf{R}$, 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": []
+    },
+    "023975": {
+        "id": "023975",
+        "content": "若函数 $f(x)=a x^2+2 x-3$ 在区间 $(-\\infty, 4)$ 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": []
+    },
+    "023976": {
+        "id": "023976",
+        "content": "若函数 $f(x)=x^3-a x$($a>0$) 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) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",