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编辑40071题面

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wangweiye7840 2024-02-19 12:35:12 +08:00
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题库0.3/Problems.json
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@ -725312,7 +725312,7 @@
},
"040071": {
"id": "040071",
"content": "设常数$a \\in \\mathbf{R}$, $\\cos x=a$分别有如下情况, 写出相应的取值范围.\\\\\n(1) 方程$\\cos x=a$在$[-\\dfrac{2 \\pi}{3}, \\dfrac{\\pi}{3}]$内恰有$1$个$x$, 则$a$的取值范围为\\blank{50};\\\\\n(2) 设常数$m>-\\dfrac{2 \\pi}{3}$. 当$a=\\dfrac{1}{2}$时, 方程$\\cos x=a$在$[-\\dfrac{2 \\pi}{3}, m]$内恰有一个$x$, 则$m$的取值范围为\\blank{50};\\\\\n(3) 常数$a$使得: 对于任意常数$m>-\\dfrac{2 \\pi}{3}$, 方程$\\cos x=a$在$[-\\dfrac{2 \\pi}{3}, m]$内总是至少有一个$x$存在, 则$a$的取值范围为\\blank{50}.",
"content": "设常数$a \\in \\mathbf{R}$. \\\\\n(1) 若关于$x$的方程$\\cos x=a$在区间$[-\\dfrac{2 \\pi}{3}, \\dfrac{\\pi}{3}]$上恰有$1$个解, 则$a$的取值范围为\\blank{50};\\\\\n(2) 设常数$m>-\\dfrac{2 \\pi}{3}$. 当$a=\\dfrac{1}{2}$时, 关于$x$的方程$\\cos x=a$在区间$[-\\dfrac{2 \\pi}{3}, m]$上恰有一解, 则$m$的取值范围为\\blank{50};\\\\\n(3) 若对于任意常数$m>-\\dfrac{2 \\pi}{3}$, 关于$x$的方程$\\cos x=a$在$[-\\dfrac{2 \\pi}{3}, m]$内总是至少有一解, 则$a$的取值范围为\\blank{50}.",
"objs": [],
"tags": [
"第三单元"
@ -725324,7 +725324,8 @@
"usages": [],
"origin": "2025届高一下学期周末卷02",
"edit": [
"20230224\t王伟叶"
"20230224\t王伟叶",
"20240219\t王伟叶"
],
"same": [],
"related": [],