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{
"markdown": "\\frac{\\partial \\theta}{\\partial y} = \\lim_{h \\to 0} \\frac{\\sin(y + h) - \\sin(y)}{h}\n## ู…ุจุฑู‡ู†ุฉ\nูุนู„ ุงู„ุบูŠุฑ ุฃู† ูŠุญู…ู„ ุนู„ู‰ (ููŽู„ุง ุชูŽูƒู’ููุฑู’) ุŒ ู„ูุณุงุฏู‡ ููŠ ุงู„ู…ุนู†ู‰. ูˆุฅู† ูƒุงู† ุฑุงุฌุนุงู‹ ุฅู„ู‰ (ุฃูŽุญูŽุฏู) ู„ู… ูŠูƒู† (ููŽูŠูŽุชูŽุนูŽู„ู‘ูŽู…ููˆู†ูŽ) ุฃูŠุถุงู‹ ุฌูˆุงุจุงู‹ ู„ู‚ูˆู„ู‡ (ููŽู„ุง ุชูŽูƒู’ููุฑู’) ุŒ ู„ุฃู† ุงู„ุชู‚ุฏูŠุฑ: ู„ุง ูŠูƒู† ูƒูุฑ ูุชุนู„ู…. / ูˆุงู„ู…ุนู†ู‰: ุฅู† ูŠูƒู† ูƒูุฑ ูŠูƒู† ุชุนู„ู…ุŒ ูˆู‡ุฐุง ุบูŠุฑ ุตุญูŠุญุŒ ุฃู„ุง\n\\mathbb{E}[n] = \\int x f_n(x) dx\n\\sum_{j=0}^{N} \\frac{\\lambda^j}{j!} = e^{\\lambda}\n## ุจุฑู‡ุงู†\nุชุฑู‰ ุฃู†ู‡ ูŠุฌูˆุฒ ุฃู† ูŠูƒูุฑ ูˆู„ุง ูŠุชุนู„ู…ุŒ ูู„ูŠุณ ุงู„ุฃูˆู„ ุณุจุจุงู‹ ู„ู„ุซุงู†ูŠุŒ ูุฅุฐุง ู„ู… ูŠุฌุฒ ุฐู„ูƒ ู„ู… ูŠุฎู„ ู…ู† ุฃุญุฏ ุฃู…ุฑูŠู†: ุฅู…ุง ุฃู† ุชุฌุนู„ ุงู„ูุนู„\n\\iint_{D} \\mu^2 \\cdot \\alpha^2 \\, dx \\, dy\n## ู†ุธุฑูŠุฉ\nู…ุนุทูˆูุงู‹ ุจุงู„ูุงุก ุนู„ู‰ ูุนู„ ู‚ุจู„ู‡ ูˆุฅู…ุง ุฃู† ู†ุฌุนู„ู‡ ุฎุจุฑุงู‹ ู„ู…ุจุชุฏุฃ ู…ุญุฐูˆู. ูˆุงู„ูุนู„ ุงู„ุฐูŠ ู‚ุจู„ู‡ ู„ุง ูŠุฎู„ูˆ ู…ู† ุฃู† ูŠูƒูˆู† (ูƒูŽููŽุฑููˆุง) ุฃูˆ (ูŠูุนูŽู„ู‘ูู…ููˆู†ูŽ) ุฃูˆ (ูŠูุนูŽู„ู‘ูู…ุงู†ู) ุŒ ุฃูˆ ูุนู„ุง ู…ู‚ุฏุฑุงู‹ ู…ุญุฐูˆูุงู‹ ู…ู† ุงู„ู„ูุธุŒ ูˆู‡ูˆ\n\\vec{F} = m\\vec{a}\n## ุชุนุฑูŠู\nยซูŠุฃุจูˆู†ยป . ูุฅู† ุนุทูุช ุนู„ู‰ ยซูƒูุฑูˆุงยป ุฌุงุฒุŒ ูˆูŠูƒูˆู† ู…ูˆุถุนู‡ ุฑูุนุงู‹ ูƒู…ูˆุถุน ยซูƒูุฑูˆุงยป . ูˆุฅู† ุนุทูุช ุนู„ู‰ (ูŠูุนูŽู„ู‘ูู…ููˆู†ูŽ ุงู„ู†ู‘ูŽุงุณูŽ) ููŠุชุนู„ู…ูˆู†ุŒ ุฌุงุฒ. ูˆ (ูŠูุนูŽู„ู‘ูู…ููˆู†ูŽ ุงู„ู†ู‘ูŽุงุณูŽ) ูŠุฌูˆุฒ ุฃู† ูŠูƒูˆู† ู…ู†ุตูˆุจุงู‹ ุนู„ู‰ ุงู„ุญุงู„ ู…ู† ุงู„ูˆุงูˆ ููŠ (ูƒูŽููŽุฑููˆุง) . ูˆูŠุฌูˆุฒ ุฃู† ูŠูƒูˆู† ุจุฏู„ุงู‹ ุนู† (ูƒูŽููŽุฑููˆุง) ุŒ ู„ุฃู† ุชุนู„ูŠู… ุงู„ุณุญุฑ ูƒูุฑ.\n\\mathbb{E}[z] = \\int x f_z(x) dx + \\frac{\\beta}{\\mu^2}\n## ุชุนุฑูŠู\n5377 - [ู… ุฏ ุณ] ุญุฏูŠุซ ูˆู‚ุช ุงู„ุธู‡ุฑ ุฅุฐุง ุฒุงู„ุช ุงู„ุดู…ุณ โ€ฆ ุงู„ุญุฏูŠุซ. (2: 210ุŒ 223) ุนู† ุนุจุฏ ุงู„ุตู…ุฏ ูˆุนูุงู†ุŒ ุนู† ู‡ู…ุงู…ุŒ ุนู† ู‚ุชุงุฏุฉ ุนู†ู‡ ุจู‡. (2: 213) ูˆุนู† ูŠุญูŠู‰ ุจู† ุฃุจูŠ ุจูƒูŠุฑุŒ ุนู† ุดุนุจุฉุŒ ุนู† ู‚ุชุงุฏุฉ ู†ุญูˆู‡. [ุชุญูุฉ 6: 388 - 389 ุญุฏูŠุซ 8946]\n\\theta_{n+1} = \\theta_n - \\alpha \\nabla f(\\theta_n)\n## ุจุฑู‡ุงู†\nู‚ุฑุงุชูƒูŠู† ุจู† ุงู„ุฃุณุนุฏ ุฃู†ุง ุฃุจูˆ ู…ุญู…ุฏ ุงู„ุฌูˆู‡ุฑูŠ ุฃู†ุง ุฃุจูˆ ุงู„ุญุณู† ุจู† ู„ุคู„ุค ู†ุง ู…ุญู…ุฏ ุจู† ุงู„ุญุณูŠู† ุจู† ุดู‡ุฑูŠุงุฑ ู†ุง ุฃุจูˆ ุญูุต ุงู„ูู„ุงุณ ูู‚ุงู„ ูˆู…ุงุช ุณุนูŠุฏ ุจู† ุฒูŠุฏ ุจู†\n\\sum_{\\mu=0}^{M} \\frac{t^\\mu}{\\mu!} = e^{t}",
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"content": "ูุนู„ ุงู„ุบูŠุฑ ุฃู† ูŠุญู…ู„ ุนู„ู‰ (ููŽู„ุง ุชูŽูƒู’ููุฑู’) ุŒ ู„ูุณุงุฏู‡ ููŠ ุงู„ู…ุนู†ู‰. ูˆุฅู† ูƒุงู† ุฑุงุฌุนุงู‹ ุฅู„ู‰ (ุฃูŽุญูŽุฏู) ู„ู… ูŠูƒู† (ููŽูŠูŽุชูŽุนูŽู„ู‘ูŽู…ููˆู†ูŽ) ุฃูŠุถุงู‹ ุฌูˆุงุจุงู‹ ู„ู‚ูˆู„ู‡ (ููŽู„ุง ุชูŽูƒู’ููุฑู’) ุŒ ู„ุฃู† ุงู„ุชู‚ุฏูŠุฑ: ู„ุง ูŠูƒู† ูƒูุฑ ูุชุนู„ู…. / ูˆุงู„ู…ุนู†ู‰: ุฅู† ูŠูƒู† ูƒูุฑ ูŠูƒู† ุชุนู„ู…ุŒ ูˆู‡ุฐุง ุบูŠุฑ ุตุญูŠุญุŒ ุฃู„ุง",
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"content": "\\mathbb{E}[n] = \\int x f_n(x) dx",
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"content": "\\sum_{j=0}^{N} \\frac{\\lambda^j}{j!} = e^{\\lambda}",
"type": "text",
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"content": "ุจุฑู‡ุงู†",
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"top_left_x": 52,
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"content": "ุชุฑู‰ ุฃู†ู‡ ูŠุฌูˆุฒ ุฃู† ูŠูƒูุฑ ูˆู„ุง ูŠุชุนู„ู…ุŒ ูู„ูŠุณ ุงู„ุฃูˆู„ ุณุจุจุงู‹ ู„ู„ุซุงู†ูŠุŒ ูุฅุฐุง ู„ู… ูŠุฌุฒ ุฐู„ูƒ ู„ู… ูŠุฎู„ ู…ู† ุฃุญุฏ ุฃู…ุฑูŠู†: ุฅู…ุง ุฃู† ุชุฌุนู„ ุงู„ูุนู„",
"type": "text",
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},
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"top_left_x": 52,
"top_left_y": 441,
"bottom_right_x": 750,
"bottom_right_y": 496,
"content": "\\iint_{D} \\mu^2 \\cdot \\alpha^2 \\, dx \\, dy",
"type": "text",
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"reading_index": 8
},
{
"top_left_x": 52,
"top_left_y": 540,
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"bottom_right_y": 570,
"content": "ู†ุธุฑูŠุฉ",
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},
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"top_left_x": 52,
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"content": "ู…ุนุทูˆูุงู‹ ุจุงู„ูุงุก ุนู„ู‰ ูุนู„ ู‚ุจู„ู‡ ูˆุฅู…ุง ุฃู† ู†ุฌุนู„ู‡ ุฎุจุฑุงู‹ ู„ู…ุจุชุฏุฃ ู…ุญุฐูˆู. ูˆุงู„ูุนู„ ุงู„ุฐูŠ ู‚ุจู„ู‡ ู„ุง ูŠุฎู„ูˆ ู…ู† ุฃู† ูŠูƒูˆู† (ูƒูŽููŽุฑููˆุง) ุฃูˆ (ูŠูุนูŽู„ู‘ูู…ููˆู†ูŽ) ุฃูˆ (ูŠูุนูŽู„ู‘ูู…ุงู†ู) ุŒ ุฃูˆ ูุนู„ุง ู…ู‚ุฏุฑุงู‹ ู…ุญุฐูˆูุงู‹ ู…ู† ุงู„ู„ูุธุŒ ูˆู‡ูˆ",
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},
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"bottom_right_y": 664,
"content": "\\vec{F} = m\\vec{a}",
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},
{
"top_left_x": 52,
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"bottom_right_y": 738,
"content": "ุชุนุฑูŠู",
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},
{
"top_left_x": 52,
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"bottom_right_y": 788,
"content": "ยซูŠุฃุจูˆู†ยป . ูุฅู† ุนุทูุช ุนู„ู‰ ยซูƒูุฑูˆุงยป ุฌุงุฒุŒ ูˆูŠูƒูˆู† ู…ูˆุถุนู‡ ุฑูุนุงู‹ ูƒู…ูˆุถุน ยซูƒูุฑูˆุงยป . ูˆุฅู† ุนุทูุช ุนู„ู‰ (ูŠูุนูŽู„ู‘ูู…ููˆู†ูŽ ุงู„ู†ู‘ูŽุงุณูŽ) ููŠุชุนู„ู…ูˆู†ุŒ ุฌุงุฒ. ูˆ (ูŠูุนูŽู„ู‘ูู…ููˆู†ูŽ ุงู„ู†ู‘ูŽุงุณูŽ) ูŠุฌูˆุฒ ุฃู† ูŠูƒูˆู† ู…ู†ุตูˆุจุงู‹ ุนู„ู‰ ุงู„ุญุงู„ ู…ู† ุงู„ูˆุงูˆ ููŠ (ูƒูŽููŽุฑููˆุง) . ูˆูŠุฌูˆุฒ ุฃู† ูŠูƒูˆู† ุจุฏู„ุงู‹ ุนู† (ูƒูŽููŽุฑููˆุง) ุŒ ู„ุฃู† ุชุนู„ูŠู… ุงู„ุณุญุฑ ูƒูุฑ.",
"type": "text",
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},
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"bottom_right_x": 750,
"bottom_right_y": 848,
"content": "\\mathbb{E}[z] = \\int x f_z(x) dx + \\frac{\\beta}{\\mu^2}",
"type": "text",
"confidence_scores": null,
"reading_index": 14
},
{
"top_left_x": 52,
"top_left_y": 892,
"bottom_right_x": 750,
"bottom_right_y": 922,
"content": "ุชุนุฑูŠู",
"type": "title",
"confidence_scores": null,
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},
{
"top_left_x": 52,
"top_left_y": 927,
"bottom_right_x": 750,
"bottom_right_y": 972,
"content": "5377 - [ู… ุฏ ุณ] ุญุฏูŠุซ ูˆู‚ุช ุงู„ุธู‡ุฑ ุฅุฐุง ุฒุงู„ุช ุงู„ุดู…ุณ โ€ฆ ุงู„ุญุฏูŠุซ. (2: 210ุŒ 223) ุนู† ุนุจุฏ ุงู„ุตู…ุฏ ูˆุนูุงู†ุŒ ุนู† ู‡ู…ุงู…ุŒ ุนู† ู‚ุชุงุฏุฉ ุนู†ู‡ ุจู‡. (2: 213) ูˆุนู† ูŠุญูŠู‰ ุจู† ุฃุจูŠ ุจูƒูŠุฑุŒ ุนู† ุดุนุจุฉุŒ ุนู† ู‚ุชุงุฏุฉ ู†ุญูˆู‡. [ุชุญูุฉ 6: 388 - 389 ุญุฏูŠุซ 8946]",
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},
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"top_left_x": 52,
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"bottom_right_x": 750,
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"content": "\\theta_{n+1} = \\theta_n - \\alpha \\nabla f(\\theta_n)",
"type": "text",
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},
{
"top_left_x": 52,
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"bottom_right_x": 750,
"bottom_right_y": 1091,
"content": "ุจุฑู‡ุงู†",
"type": "title",
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},
{
"top_left_x": 52,
"top_left_y": 1096,
"bottom_right_x": 750,
"bottom_right_y": 1140,
"content": "ู‚ุฑุงุชูƒูŠู† ุจู† ุงู„ุฃุณุนุฏ ุฃู†ุง ุฃุจูˆ ู…ุญู…ุฏ ุงู„ุฌูˆู‡ุฑูŠ ุฃู†ุง ุฃุจูˆ ุงู„ุญุณู† ุจู† ู„ุคู„ุค ู†ุง ู…ุญู…ุฏ ุจู† ุงู„ุญุณูŠู† ุจู† ุดู‡ุฑูŠุงุฑ ู†ุง ุฃุจูˆ ุญูุต ุงู„ูู„ุงุณ ูู‚ุงู„ ูˆู…ุงุช ุณุนูŠุฏ ุจู† ุฒูŠุฏ ุจู†",
"type": "text",
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},
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"content": "\\sum_{\\mu=0}^{M} \\frac{t^\\mu}{\\mu!} = e^{t}",
"type": "text",
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}
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