dataset / data /run_test_2_002 /annotations /sample_0000244.json
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"markdown": "ุงู„ุทุจ ุงู„ูˆู‚ุงุฆูŠ ูˆุงู„ุตุญุฉ ุงู„ู…ุฌุชู…ุนูŠุฉ\n\\sum_{j=0}^{100} \\frac{z^j}{j!} = e^{z}\nุงู„ู…ุนุทูŠุงุช ูˆุงู„ุญู‚ุงุฆู‚ ุงู„ุฃุณุงุณูŠุฉ\nู…ู†ุจู‡ 286 ู‰ ูŠุฒูŠุฏ ุจู† ุนุจุฏ ุงู„ู…ู„ูƒ 337ุŒ 337ุŒ 338 393ุŒ 497 ูŠุฒูŠุฏ ุจู† ู…ุนุงูˆูŠุฉ 69ุŒ 75ุŒ 78ุŒ 85ุŒ 86ุŒ 492 ูŠุฒูŠุฏ ุจู† ุงู„ู…ู‡ู„ุจ 203ุŒ 204ุŒ 260 ูŠุฒูŠุฏ ุจู† ุงู„ูˆู„ูŠุฏ ุจู† ุนุจุฏ ุงู„ู…ู„ูƒ 97ุŒ 398 402ุŒ 498 ูŠูˆุณู ุจู† ุนู…ุฑ ุงู„ุซู‚ูู‰ 357ุŒ 359ุŒ 365 366ุŒ 473 ุชู… ูู‡ุฑุณ ุงู„ูƒุชุงุจ\n## ุชุนุฑูŠู\n\\iint_{D} \\mu^2 \\geq k^2 \\, dx \\, dy\nุชุดุฑู‚ ุงู„ุดู…ุณ ูˆู…ุง ุฃู†ุง ุจู…ุชุฎู„ู ุนู† ุงู„ุนู†ู‚ (3) ุงู„ุฃูˆู„ ุจุนุฏ ุฅุฐ ุณู…ุนุช ุฑุณูˆู„ ุงู„ู„ู‡ ุตู„ู‰ ุงู„ู„ู‡ ุนู„ูŠู‡ ูˆุณู„ู… ูŠู‚ูˆู„ ูŠุฌุฆ ูู‚ุฑุงุก ุงู„ู…ุณู„ู…ูŠู† ูŠุฏููˆู† (4) ูƒู…ุง ูŠุฏู ุงู„ุญู…ุงู… ูู‚ุงู„ ู„ู‡ู… ู‚ููˆุง ู„ู„ุญุณุงุจ ููŠู‚ูˆู„ูˆู† ูˆุงู„ู„ู‡ ู…ุง ุชุฑูƒู†ุง ุดูŠุฆุง ู†ุญุงุณุจ ุจู‡ ููŠู‚ูˆู„ ุงู„ู„ู‡ ุตุฏู‚ ุนุจุงุฏูŠ ููŠุฏุฎู„ูˆู† ุงู„ุฌู†ุฉ ู‚ุจู„ ุงู„ู†ุงุณ ุจุณุจุนูŠู† ุนุงู…ุง (5) ูˆู‚ุฏ ุฑูˆู‰ ุงู„ุดุนุจูŠ ุจุนุถ ุงู„ู‚ุตุฉ ูˆู„ู… ูŠุณู†ุฏ ู…ู†ู‡ุง ุดูŠุฆุง ุฃุฎุจุฑู†ุง ุฃุจูˆ ุงู„ู‚ุงุณู… ุงู„ุดุญุงู…ูŠ ุฃู†ุง ุฃุจูˆ ุณุนุฏ ุงู„ุฌู†ุฒุฑูˆุฏูŠ (6) ุฃู†ุง ุงู„ุญุงูƒู… ุฃุจูˆ ุฃุญู…ุฏ ุฃู†ุง ุฃุจูˆ ุฌุนูุฑ ู…ุญู…ุฏ ุจู† ุงู„ุญุณูŠู† ุงู„ุฎุซุนู…ูŠ ุจุงู„ูƒูˆูุฉ ู†ุง ุฌุนูุฑ ุจู† ู…ุญู…ุฏ ุจู† ุนุจุฏ ุงู„ุณู„ุงู… ู†ุง ุฃุจูˆ ู…ุนุงูˆูŠุฉ ุนู† ู…ูˆุณู‰ ุงู„ุตุบูŠุฑ ุนู† ุนุจุฏ ุงู„ุฑุญู…ู† ุจู† ุณุงุจุท ุนู† ุณุนูŠุฏ ุจู† ุญุฐูŠู… ู‚ุงู„\n\n![image](img-0)\n\nุงู„ุดูƒู„ (4): ู…ู‚ุงุฑู†ุฉ ุจูŠู† ุงู„ุขู„ูŠุงุช ูˆุงู„ุฅุฌุฑุงุกุงุช ุงู„ู…ุชุจุนุฉ ูˆู…ู†ู‡ุฌูŠุฉ ุงู„ุจุญุซ ูˆุฃุฏูˆุงุช ุฌู…ุน ุงู„ุจูŠุงู†ุงุช\nx_{n+1} = x_n - \\alpha \\nabla f(x_n)\nุงู„ุฎุงุชู…ุฉ ูˆุงู„ุงุณุชู†ุชุงุฌุงุช ุงู„ู†ู‡ุงุฆูŠุฉ\nุงู„ู…ุดุชุฑูŠ ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู† ูˆุจุงู„ู…ู‡ุฑ ูˆู‚ูŠู…ุฉ ุงู„ูˆู„ุฏ ุฎู„ุงูุงู‹ ู„ู„ุญู†ููŠู‘ุฉ ููŠ ุงู„ู…ู‡ุฑ. ูˆู…ู†ู‡ุง: ุฑุฌู„ ุชุณุญู‘ุฑ ููŠ ุดู‡ุฑ ุฑู…ุถุงู† ูˆู‚ุฏ ุทู„ุน ุงู„ูุฌุฑ - ูˆู‡ูˆ ู„ุง ูŠุนู„ู… ุจู‡ - ูุนู†ุฏ ุงู„ุญู†ููŠู‘ุฉ ูุณุฏ ุตูˆู…ู‡ุŒ ูˆุนู†ุฏ ุงุจู† ุฃุจูŠ ู„ูŠู„ู‰ ุตุญู‘ ุตูˆู…ู‡ ู‚ูŠุงุณุงู‹ ุนู„ู‰ ุงู„ู†ู‘ุงุณูŠ. ูˆุนู†ุฏ ุงู„ุญู†ููŠุฉ: ุฅู†ู‘ ุงู„ู…ุฎุทุฆ ู„ูŠุณ ูƒุงู„ู†ู‘ุงุณูŠุ› ู„ุฃู†ู‘\n\n![image](img-1)\n\nุงู„ุดูƒู„ (2): ู…ุฎุฑุฌุงุช ู†ู…ูˆุฐุฌ ุชุญู„ูŠู„ ุงู„ู…ุชุบูŠุฑุงุช ูˆุงู„ุนูˆุงู…ู„ ุงู„ู…ุคุซุฑุฉ\n\n![image](img-2)\n\nู…ุฎุทุท ุงู†ุณูŠุงุจูŠ ู„ุฅุฌุฑุงุกุงุช ุงู„ุฎุงุชู…ุฉ ูˆุงู„ุงุณุชู†ุชุงุฌุงุช ุงู„ู†ู‡ุงุฆูŠุฉ\n\n![image](img-3)\n\nุงู„ุดูƒู„ (1): ูŠูˆุถุญ ุชูˆุฒูŠุน ุงู„ุฅุทุงุฑ ุงู„ู†ุธุฑูŠ ูˆุงู„ู…ูุงู‡ูŠู…ูŠ ู„ู„ุฏุฑุงุณุฉ\n\n[tbl-0.html](tbl-0.html)\n\nุงู„ู…ุณุชุฌุฏุงุช ูˆุงู„ุชุทูˆุฑุงุช ุงู„ุฑุงู‡ู†ุฉ\n\\iint_{D} y^2 - \\theta^2 \\, dx \\, dy",
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"content": "<table><tbody><tr><th>ุนู† ุงู„ุญู‚ ูˆุงู„ุฒู…</th><th>ุงู„ุฃู…ุฑ ุฐุง ุงู„ุญุฌุฉ</th><th>ูŠุนู†ูƒ</th></tr><tr><td>ุงู„ู„ู‡ ุนู„ู‰ ู…ุง ูˆู„ุงูƒ</td><td>ูˆุฎุถ ุงู„ุบู…ุฑุงุช ุฅู„ู‰ ุงู„ุญู‚</td><td>ุญูŠุซ ุนู„ู…ุชู‡ ูˆู„ุง ุชุฎุด</td></tr><tr><td>ููŠ ุงู„ู„ู‡ ู„ูˆู…ุฉ ู„ุงุฆู… (1) ู‚ุงู„ ูู‚ุงู„ ุนู…ุฑ</td><td>ูˆูŠุญูƒ ูŠุง ุณุนูŠุฏ</td><td>ุจู† ู…ู† ูŠุทูŠู‚ ู‡ุฐุง ู‚ุงู„</td></tr><tr><td>ู…ู† ู‚ุทุน (2) ุงู„ู„ู‡</td><td>ููŠ ุนู†ู‚ู‡</td><td>ู…ุซู„ ุงู„ุฐูŠ ูˆุถุน ููŠ ุนู†ู‚ูƒ ุฅู†ู…ุง ุนู„ูŠูƒ ุฃู†</td></tr><tr><td>ุชุฃู…ุฑ ููŠุทุงุน ุฃู…ุฑูƒ ูˆุชุชุฑูƒ ููŠูƒูˆู† ู„ูƒ ุงู„ุญุฌุฉ ู‚ุงู„</td><td>ูู‚ุงู„ ุนู…ุฑ ุฅู†ุง ุณู†ุฌุนู„ ู„ูƒ</td><td>ุฑุฒู‚ุง ู‚ุงู„ ู„ู‚ุฏ ุฃุนุทูŠุช</td></tr><tr><td>ู…ุง ูŠูƒููŠู†ูŠ ุฏูˆู†ู‡ ูŠุนู†ูŠ ุนุทุงุกู‡</td><td>ูˆู…ุง ุฃู†ุง</td><td>ุจู…ุฒุฏุงุฏ ู…ู† ู…ุงู„ ุงู„ู…ุณู„ู…ูŠู† ุดูŠุฆุง ู‚ุงู„</td></tr></tbody></table>",
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"text": "ุนู†",
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"text": " ุงู„ุญู‚",
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"text": " ูˆุงู„ุฒู…",
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{
"text": "ุงู„ุฃู…ุฑ",
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{
"text": " ุฐุง",
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"text": " ุงู„ุญุฌุฉ",
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"text": "ูŠุนู†ูƒ",
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"text": "ุงู„ู„ู‡",
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"text": " ุนู„ู‰",
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"text": " ู‡ุฐุง",
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"content": "ุงู„ุดูƒู„ (4): ู…ู‚ุงุฑู†ุฉ ุจูŠู† ุงู„ุขู„ูŠุงุช ูˆุงู„ุฅุฌุฑุงุกุงุช ุงู„ู…ุชุจุนุฉ ูˆู…ู†ู‡ุฌูŠุฉ ุงู„ุจุญุซ ูˆุฃุฏูˆุงุช ุฌู…ุน ุงู„ุจูŠุงู†ุงุช",
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"content": "ุงู„ุฎุงุชู…ุฉ ูˆุงู„ุงุณุชู†ุชุงุฌุงุช ุงู„ู†ู‡ุงุฆูŠุฉ",
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"content": "ุงู„ู…ุดุชุฑูŠ ูŠุฑุฌุน ุนู„ู‰ ุงู„ุจุงุฆุน ุจุงู„ุซู‘ู…ู† ูˆุจุงู„ู…ู‡ุฑ ูˆู‚ูŠู…ุฉ ุงู„ูˆู„ุฏ ุฎู„ุงูุงู‹ ู„ู„ุญู†ููŠู‘ุฉ ููŠ ุงู„ู…ู‡ุฑ. ูˆู…ู†ู‡ุง: ุฑุฌู„ ุชุณุญู‘ุฑ ููŠ ุดู‡ุฑ ุฑู…ุถุงู† ูˆู‚ุฏ ุทู„ุน ุงู„ูุฌุฑ - ูˆู‡ูˆ ู„ุง ูŠุนู„ู… ุจู‡ - ูุนู†ุฏ ุงู„ุญู†ููŠู‘ุฉ ูุณุฏ ุตูˆู…ู‡ุŒ ูˆุนู†ุฏ ุงุจู† ุฃุจูŠ ู„ูŠู„ู‰ ุตุญู‘ ุตูˆู…ู‡ ู‚ูŠุงุณุงู‹ ุนู„ู‰ ุงู„ู†ู‘ุงุณูŠ. ูˆุนู†ุฏ ุงู„ุญู†ููŠุฉ: ุฅู†ู‘ ุงู„ู…ุฎุทุฆ ู„ูŠุณ ูƒุงู„ู†ู‘ุงุณูŠุ› ู„ุฃู†ู‘",
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"content": "ุงู„ุดูƒู„ (2): ู…ุฎุฑุฌุงุช ู†ู…ูˆุฐุฌ ุชุญู„ูŠู„ ุงู„ู…ุชุบูŠุฑุงุช ูˆุงู„ุนูˆุงู…ู„ ุงู„ู…ุคุซุฑุฉ",
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"content": "ู…ุฎุทุท ุงู†ุณูŠุงุจูŠ ู„ุฅุฌุฑุงุกุงุช ุงู„ุฎุงุชู…ุฉ ูˆุงู„ุงุณุชู†ุชุงุฌุงุช ุงู„ู†ู‡ุงุฆูŠุฉ",
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"content": "ุงู„ุดูƒู„ (1): ูŠูˆุถุญ ุชูˆุฒูŠุน ุงู„ุฅุทุงุฑ ุงู„ู†ุธุฑูŠ ูˆุงู„ู…ูุงู‡ูŠู…ูŠ ู„ู„ุฏุฑุงุณุฉ",
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"content": "\\iint_{D} y^2 - \\theta^2 \\, dx \\, dy",
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