添加三道题, 第3题是关联题

题库0.3/Problems.json

@@ -90288,7 +90288,9 @@
             "20220701\t王伟叶"
         ],
         "same": [],
-        "related": [],
+        "related": [
+            "022910"
+        ],
         "remark": "",
         "space": "4em",
         "unrelated": []
@@ -609853,6 +609855,75 @@
         "space": "4em",
         "unrelated": []
     },
+    "022908": {
+        "id": "022908",
+        "content": "已知函数$y=\\ln x-(\\dfrac{1}{2})^x+x^3-3$唯一的零点在区间$(d,d+0.1)$中, 且$10d\\in \\mathbf{Z}$, 则$n=$\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231204\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "022909": {
+        "id": "022909",
+        "content": "证明: 函数$y=x+\\dfrac{4}{x}$在$[2,+\\infty)$上是严格增函数.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "自拟题目",
+        "edit": [
+            "20231204\t王伟叶"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "022910": {
+        "id": "022910",
+        "content": "设$a$是常数, $f(x)=\\mathrm{e}^x+\\dfrac a{\\mathrm{e}^x}$, 且函数$y=f(x)$是偶函数.\\\\\n(1) 求$a$的值;\\\\\n(2) 求证: 函数$y=f(x)$在$\\mathbf{R}$上不是增函数;\\\\\n(3) 求证: 函数$y=f(x)$在$[0,+\\infty)$上是增函数.",
+        "objs": [
+            "K0219003B"
+        ],
+        "tags": [
+            "第二单元",
+            "2023届高三-寒假作业-中档题",
+            "2023届高三-第一轮复习讲义-08-函数的单调性"
+        ],
+        "genre": "4em",
+        "ans": "(1); $a=1$; (2) 证明略; (3) 证明略",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2022届高三第一轮复习讲义-20231204修改",
+        "edit": [
+            "20220701\t王伟叶",
+            "20231204\t王伟叶"
+        ],
+        "same": [],
+        "related": [
+            "002894"
+        ],
+        "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.",