math-ai/BlueMO
BlueMO 🚀 BlueMO: A Comprehensive Collection of Challenging Mathematical Olympiad Problems from the Little Blue Book Series BlueMO is a comprehensive and challenging dataset comprising mathematical olympiad problems paired with detailed solutions, meticulously curated from the esteemed "Little Blue Book" (小蓝书) series (Second Edition)—a vital resource for Chinese students training for national and international olympiad math competitions. Designed to… See the full description on the dataset page: https://huggingface.co/datasets/math-ai/BlueMO.
39.7k
1{2 "source_file": "./raw_volume-zh/volume2/exercise7.tex",3 "problem_type": "calculation",4 "problem": "问题1 求函数方程:\n$$\n2 f(x)+x^2 f\\left(\\frac{1}{x}\\right)=\\sin x(x>0)\n$$\n在 $(0,+\\infty)$ 上的解.",5 "solution": "将函数方程中的 $x$ 用 $\\frac{1}{x}$ 代换, 得 $2 f\\left(\\frac{1}{x}\\right)+\\frac{1}{x^2} f(x)=\\sin \\frac{1}{x}$, 即 $f(x)+ 2 x^2 f\\left(\\frac{1}{x}\\right)=x^2 \\sin \\frac{1}{x}$. 将上面方程与原方程联立消去 $f\\left(\\frac{1}{x}\\right)$, 得 $f(x)= \\frac{2}{3}\\left(\\sin x-\\frac{x^2}{2} \\sin \\frac{1}{x}\\right)$.",6 "remark": "",7 "figures": []8}