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修改14785题面

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weiye.wang 2023-06-21 22:36:25 +08:00
parent 3860bf8584
commit cb7992a403
2 changed files with 4 additions and 3 deletions
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2
工具/latex界面修改题目内容.py
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@ -1,6 +1,6 @@
import os,re,json
"""这里编辑题号(列表)后将在vscode中打开窗口, 编辑后保存关闭"""
problems = "14697"
problems = "14758"
editor = "王伟叶"
def generate_number_set(string,dict):

5
题库0.3/Problems.json
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@ -388980,7 +388980,7 @@
},
"014758": {
"id": "014758",
"content": "数学家们在探寻自然对数底$\\mathrm{e} \\approx 2.71828$与圆周率$\\pi$之间的联系时, 发现了以下公式($\\mathrm{i}$为虚数单位):\\\\\n(I) $\\mathrm{e}^x=1+\\dfrac{x}{1 !}+\\dfrac{x^2}{2 !}+\\dfrac{x^3}{3 !}+\\cdots+\\dfrac{x^n}{n !}+\\cdots$;\\\\\n(II) $\\sin x=\\dfrac{x}{1 !}-\\dfrac{x^3}{3 !}+\\dfrac{x^5}{5 !}-\\dfrac{x^7}{7 !}+\\cdots+(-1)^{n-1} \\dfrac{x^{2 n-1}}{(2 n-1) !}+\\cdots$;\\\\\n(III) $\\cos x=1-\\dfrac{x^2}{2 !}+\\dfrac{x^4}{4 !}-\\dfrac{x^6}{6 !}+\\cdots+(-1)^{n-1} \\dfrac{x^{2 n-2}}{(2 n-2) !}+\\cdots$.\\\\\n上述公式中, $x \\in \\mathbf{C}$, $n \\in \\mathbf{N}$, $n\\ge 1$, 据此判断, 当$x\\in \\mathbf{C}$时, 以下命题\n\\textcircled{1} $\\mathrm{e}^{\\mathrm{i}x}=\\cos x+\\mathrm{i} \\sin x$; \n\\textcircled{2} $\\mathrm{e}^{\\mathrm{i}x}=\\sin x+\\mathrm{i} \\cos x$; \n\\textcircled{3} $\\mathrm{e}^{\\mathrm{i} \\pi}+1=0$; \n\\textcircled{4} $\\mathrm{e}^{\\mathrm{i} \\pi}+i=0$; \n\\textcircled{5} $|\\mathrm{e}^{\\mathrm{i}x}+\\mathrm{e}^{-\\mathrm{i}x}| \\leq 2$中, 正确的个数是\\bracket{20}.\n\\fourch{$1$个}{$2$个}{$3$个}{$4$个}",
"content": "数学家们在探寻自然对数底$\\mathrm{e} \\approx 2.71828$与圆周率$\\pi$之间的联系时, 发现了以下公式($\\mathrm{i}$为虚数单位):\\\\\n(I) $\\mathrm{e}^x=1+\\dfrac{x}{1 !}+\\dfrac{x^2}{2 !}+\\dfrac{x^3}{3 !}+\\cdots+\\dfrac{x^n}{n !}+\\cdots$;\\\\\n(II) $\\sin x=\\dfrac{x}{1 !}-\\dfrac{x^3}{3 !}+\\dfrac{x^5}{5 !}-\\dfrac{x^7}{7 !}+\\cdots+(-1)^{n-1} \\dfrac{x^{2 n-1}}{(2 n-1) !}+\\cdots$;\\\\\n(III) $\\cos x=1-\\dfrac{x^2}{2 !}+\\dfrac{x^4}{4 !}-\\dfrac{x^6}{6 !}+\\cdots+(-1)^{n-1} \\dfrac{x^{2 n-2}}{(2 n-2) !}+\\cdots$.\\\\\n上述公式中, $x \\in \\mathbf{C}$, $n \\in \\mathbf{N}$, $n\\ge 1$, 据此判断, 当$x\\in \\mathbf{C}$时, 以下命题\n\\textcircled{1} $\\mathrm{e}^{\\mathrm{i}x}=\\cos x+\\mathrm{i} \\sin x$; \n\\textcircled{2} $\\mathrm{e}^{\\mathrm{i}x}=\\sin x+\\mathrm{i} \\cos x$; \n\\textcircled{3} $\\mathrm{e}^{\\mathrm{i} \\pi}+1=0$; \n\\textcircled{4} $\\mathrm{e}^{\\mathrm{i} \\pi}+\\mathrm{i}=0$; \n\\textcircled{5} $|\\mathrm{e}^{\\mathrm{i}x}+\\mathrm{e}^{-\\mathrm{i}x}| \\leq 2$中, 正确的个数是\\bracket{20}.\n\\fourch{$1$个}{$2$个}{$3$个}{$4$个}",
"objs": [],
"tags": [],
"genre": "选择题",
@ -389003,7 +389003,8 @@
],
"origin": "23届宝山区混合式教学适应性练习试题16",
"edit": [
"20230314\t王伟叶"
"20230314\t王伟叶",
"20230621\t王伟叶"
],
"same": [],
"related": [],