录入2025届高二下学期校本作业-导数 新题

工具v2/文本文件/pendingmetadata.txt

@@ -0,0 +1,2 @@
+usages
+

题库0.3/Problems.json

@@ -580630,7 +580630,9 @@
         "edit": [
             "20230101\t王伟叶"
         ],
-        "same": [],
+        "same": [
+            "041043"
+        ],
         "related": [],
         "remark": "",
         "space": "",
@@ -581945,7 +581947,9 @@
         "edit": [
             "20230101\t王伟叶"
         ],
-        "same": [],
+        "same": [
+            "041046"
+        ],
         "related": [],
         "remark": "",
         "space": "4em",
@@ -707280,7 +707284,9 @@
             "20230101\t王伟叶",
             "20230321\t王伟叶"
         ],
-        "same": [],
+        "same": [
+            "041045"
+        ],
         "related": [
             "021433"
         ],
@@ -750804,5 +750810,111 @@
         "remark": "",
         "space": "4em",
         "unrelated": []
+    },
+    "041042": {
+        "id": "041042",
+        "content": "已知曲线 $C: f(x)=x^3+x$.\\\\\n    (1) 求曲线 $C$ 在点 $(1,2)$ 处切线的方程:\\\\\n    (2) 设曲线上任意一点处切线的侧斜角为 $\\alpha$, 求 $\\alpha$ 的取值范围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高二下学期校本作业-导数",
+        "edit": [
+            "20240224\t蔡海鸾"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
+    },
+    "041043": {
+        "id": "041043",
+        "content": "曲线 $y=x \\ln x$ 上的点到直线 $x-y-2=0$ 的最短距离为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高二下学期校本作业-导数",
+        "edit": [
+            "20240224\t蔡海鸾"
+        ],
+        "same": [
+            "021395"
+        ],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "041044": {
+        "id": "041044",
+        "content": "已知奇函数, $f(x)=\\begin{cases}\\dfrac{\\mathrm{e}^x}{x}-1 & (x>0),\\\\h(x) & (x<0),\\end{cases}$ 则函数 $h(x)$ 的最大值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高二下学期校本作业-导数",
+        "edit": [
+            "20240224\t蔡海鸾"
+        ],
+        "same": [],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "041045": {
+        "id": "041045",
+        "content": "已知函数 $f(x)=a x-\\ln x$, 当 $x \\in(0, \\mathrm{e})(\\mathrm{c}$ 为自然常数 $)$ 时, 函数 $f(x)$ 的最小值为 3 , 则 $a$ 的值为\\blank{50}.",
+        "objs": [],
+        "tags": [],
+        "genre": "填空题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高二下学期校本作业-导数",
+        "edit": [
+            "20240224\t蔡海鸾"
+        ],
+        "same": [
+            "031354"
+        ],
+        "related": [],
+        "remark": "",
+        "space": "",
+        "unrelated": []
+    },
+    "041046": {
+        "id": "041046",
+        "content": "设函数 $f(x)=t x^2+2 t^2 x+t-1$($x \\in \\mathbf{R}$, $t>0$).\\\\\n    (1) 求 $f(x)$ 的最小值 $h(t)$;\\\\\n    (2) 若 $h(t)<-2 t+m$ 对 $t \\in(0,2)$ 恒成立, 求实数 $m$ 的取值萢围.",
+        "objs": [],
+        "tags": [],
+        "genre": "解答题",
+        "ans": "",
+        "solution": "",
+        "duration": -1,
+        "usages": [],
+        "origin": "2025届高二下学期校本作业-导数",
+        "edit": [
+            "20240224\t蔡海鸾"
+        ],
+        "same": [
+            "021436"
+        ],
+        "related": [],
+        "remark": "",
+        "space": "4em",
+        "unrelated": []
     }
 }