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| "markdown": "## ู ุจุฑููุฉ\nโ โ2516 - ุนู ุงุฑุฉ ุจู ุฒุงุฐุงู ุงูุตูุฏูุงููุ ุฃุจู ุณูู ุฉุ ุงูุจูุตูุฑููู . โข ูุงู ุงูุจูุฑููุงูููู: ุณูู ูุนูุชู ุงูุฏููุงุฑูููุทููููู ูููู ุนู ุงุฑุฉ ุจู ุฒุงุฐุงู ุงูุตูุฏูุงููุ ุจุตุฑู ุถุนููุ ูุง ูุนุชุจุฑ ุจู. (375) . โข ูุฐูุฑู ุงูุฏููุงุฑูููุทููููู ูู ยซุงูุถุนูุงุก ูุงูู ุชุฑููููยป (382) ุ\n\\frac{\\partial \\theta}{\\partial i} = \\lim_{h \\to 0} \\frac{\\sin(i + h) - \\sin(i)}{h}\n## ุชุนุฑูู\nููุงู ุจุตุฑูุ ุนู ุซุงุจุชุ ูุฃุจู ุบุงูุจ ุญุฒูุฑ.\nt_{n+1} = t_n - \\alpha \\nabla f(t_n)\n## ู ูุงุญุธุฉ\nุฃูุฎูุจูุฑูููุง ุฃูุจูู ุงููุนูุจููุงุณู ู ูุญูู ููุฏู ุจููู ุฃูุญูู ูุฏู ุงููู ูุญูุจููุจููููุ ุซูููุง ุณูุนููุฏู ุจููู ู ูุณูุนููุฏูุ ุซูููุง ููุฒููุฏู ุจููู ููุงุฑููููุ ุฃูููุจูุฃู ุงููุฌูุฑูููุฑููููุ ุนููู ุฃูุจูู ุงููุนูููุงุกูุ ุนููู ุนูุซูู ูุงูู ุจููู ุฃูุจูู ุงููุนูุงุตูุ\n\\int_{3}^{M} \\max(\\beta) \\, d\\beta = \\theta^2 \\approx C\n## ุจุฑูุงู\nุฑุถู ุงููู ุนูู ููุงูู: ููููุชู: ููุง ุฑูุณูููู ุงูููููู ุฅูููู ุงูุดููููุทูุงูู ููุฏู ุญูุงูู ุจูููููู ููุจููููู ุตูููุงุชูู ููููุฑูุงุกูุชูู ููููุงูู: ยซุฅูููู ุฐููููู ุดูููุทูุงูู ููููุงูู ูููู ุฎูููุฒูุจู ููุฅูุฐูุง ุฃูุญูุณูุณูุชููู ููุชูุนููููุฐู ุจูุงูููููู ู ููููู ููุงุชููููู ุนููู ููุณูุงุฑูููยป ููุงูู: ููููุนูููุชู ููุฃูุฐูููุจู ุงูููููู ุนููููู ยซููุฐูุง ุญูุฏููุซู ุตูุญููุญู ุงููุฅูุณูููุงุฏู ููููู ู\n\\iint_{D} y^2 \\leq n^2 \\, dx \\, dy\n## ุจุฑูุงู\nููุฎูุฑููุฌูุงููยป 7514 - ุตุญูุญ\n\\int_{3}^{M} \\exp(\\alpha) \\, d\\alpha = x^2 \\leq C\n## ู ุจุฑููุฉ\nูุงูุนูู ุงูุฎูุงุฑ ู ู ุงูููุงุณุ ูุงูุนูู ุงูุฌุงุณูุณ. ูู ูุงุฏ ุงููุงุนุฏุฉ: ุฃูู ุงูู ุดุชุฑู ู ู ุญูุซ ุญู ูู ุนูู ููู ู ุนุงููู ุฃู ุนูู ู ุนูู ุฏูู ุขุฎุฑ ู ุณุฃูุฉ ุฎูุงูููุฉ\n\\sum_{\\alpha=0}^{100} \\frac{z^\\alpha}{\\alpha!} = e^{z}\n\\mathbb{E}[z] = \\int x f_z(x) dx\n\\prod_{n=1}^{n} (1 \\geq y_n) = 0\n\\prod_{i=1}^{n} (1 \\leq \\beta_i) = 0", | |
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| { | |
| "text": "##", | |
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| }, | |
| { | |
| "text": "ู ุจุฑููุฉ", | |
| "confidence": 1.0, | |
| "start_index": 3 | |
| }, | |
| { | |
| "text": "โ", | |
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| }, | |
| { | |
| "text": "โ2516", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "-", | |
| "confidence": 1.0, | |
| "start_index": 18 | |
| }, | |
| { | |
| "text": "ุนู ุงุฑุฉ", | |
| "confidence": 1.0, | |
| "start_index": 20 | |
| }, | |
| { | |
| "text": "ุจู", | |
| "confidence": 1.0, | |
| "start_index": 26 | |
| }, | |
| { | |
| "text": "ุฒุงุฐุงู", | |
| "confidence": 1.0, | |
| "start_index": 29 | |
| }, | |
| { | |
| "text": "ุงูุตูุฏูุงููุ", | |
| "confidence": 1.0, | |
| "start_index": 35 | |
| }, | |
| { | |
| "text": "ุฃุจู", | |
| "confidence": 1.0, | |
| "start_index": 46 | |
| }, | |
| { | |
| "text": "ุณูู ุฉุ", | |
| "confidence": 1.0, | |
| "start_index": 50 | |
| }, | |
| { | |
| "text": "ุงูุจูุตูุฑููู", | |
| "confidence": 1.0, | |
| "start_index": 56 | |
| }, | |
| { | |
| "text": ".", | |
| "confidence": 1.0, | |
| "start_index": 67 | |
| }, | |
| { | |
| "text": "โข", | |
| "confidence": 1.0, | |
| "start_index": 69 | |
| }, | |
| { | |
| "text": "ูุงู", | |
| "confidence": 1.0, | |
| "start_index": 71 | |
| }, | |
| { | |
| "text": "ุงูุจูุฑููุงูููู:", | |
| "confidence": 1.0, | |
| "start_index": 75 | |
| }, | |
| { | |
| "text": "ุณูู ูุนูุชู", | |
| "confidence": 1.0, | |
| "start_index": 89 | |
| }, | |
| { | |
| "text": "ุงูุฏููุงุฑูููุทููููู", | |
| "confidence": 1.0, | |
| "start_index": 98 | |
| }, | |
| { | |
| "text": "ูููู", | |
| "confidence": 1.0, | |
| "start_index": 115 | |
| }, | |
| { | |
| "text": "ุนู ุงุฑุฉ", | |
| "confidence": 1.0, | |
| "start_index": 120 | |
| }, | |
| { | |
| "text": "ุจู", | |
| "confidence": 1.0, | |
| "start_index": 126 | |
| }, | |
| { | |
| "text": "ุฒุงุฐุงู", | |
| "confidence": 1.0, | |
| "start_index": 129 | |
| }, | |
| { | |
| "text": "ุงูุตูุฏูุงููุ", | |
| "confidence": 1.0, | |
| "start_index": 135 | |
| }, | |
| { | |
| "text": "ุจุตุฑู", | |
| "confidence": 1.0, | |
| "start_index": 146 | |
| }, | |
| { | |
| "text": "ุถุนููุ", | |
| "confidence": 1.0, | |
| "start_index": 151 | |
| }, | |
| { | |
| "text": "ูุง", | |
| "confidence": 1.0, | |
| "start_index": 157 | |
| }, | |
| { | |
| "text": "ูุนุชุจุฑ", | |
| "confidence": 1.0, | |
| "start_index": 160 | |
| }, | |
| { | |
| "text": "ุจู.", | |
| "confidence": 1.0, | |
| "start_index": 166 | |
| }, | |
| { | |
| "text": "(375)", | |
| "confidence": 1.0, | |
| "start_index": 170 | |
| }, | |
| { | |
| "text": ".", | |
| "confidence": 1.0, | |
| "start_index": 176 | |
| }, | |
| { | |
| "text": "โข", | |
| "confidence": 1.0, | |
| "start_index": 178 | |
| }, | |
| { | |
| "text": "ูุฐูุฑู", | |
| "confidence": 1.0, | |
| "start_index": 180 | |
| }, | |
| { | |
| "text": "ุงูุฏููุงุฑูููุทููููู", | |
| "confidence": 1.0, | |
| "start_index": 186 | |
| }, | |
| { | |
| "text": "ูู", | |
| "confidence": 1.0, | |
| "start_index": 203 | |
| }, | |
| { | |
| "text": "ยซุงูุถุนูุงุก", | |
| "confidence": 1.0, | |
| "start_index": 206 | |
| }, | |
| { | |
| "text": "ูุงูู ุชุฑููููยป", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "(382)", | |
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| { | |
| "text": "ุ", | |
| "confidence": 1.0, | |
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| { | |
| "text": "\\frac{\\partial", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "\\theta}{\\partial", | |
| "confidence": 1.0, | |
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| { | |
| "text": "=", | |
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| }, | |
| { | |
| "text": "ููุงู", | |
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| }, | |
| { | |
| "text": "ุจุตุฑูุ", | |
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| { | |
| "text": "ุนู", | |
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| { | |
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| { | |
| "text": "ูุฃุจู", | |
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| { | |
| "text": "ุบุงูุจ", | |
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| { | |
| "text": "ุญุฒูุฑ.", | |
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| { | |
| "text": "ุฃูุฎูุจูุฑูููุง", | |
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| { | |
| "text": "ุฃูุจูู", | |
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| { | |
| "text": "ุงููุนูุจููุงุณู", | |
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| }, | |
| { | |
| "text": "ู ูุญูู ููุฏู", | |
| "confidence": 1.0, | |
| "start_index": 441 | |
| }, | |
| { | |
| "text": "ุจููู", | |
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| }, | |
| { | |
| "text": "ุฃูุญูู ูุฏู", | |
| "confidence": 1.0, | |
| "start_index": 456 | |
| }, | |
| { | |
| "text": "ุงููู ูุญูุจููุจููููุ", | |
| "confidence": 1.0, | |
| "start_index": 465 | |
| }, | |
| { | |
| "text": "ุซูููุง", | |
| "confidence": 1.0, | |
| "start_index": 482 | |
| }, | |
| { | |
| "text": "ุณูุนููุฏู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ู ูุณูุนููุฏูุ", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุซูููุง", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ููุฒููุฏู", | |
| "confidence": 1.0, | |
| "start_index": 518 | |
| }, | |
| { | |
| "text": "ุจููู", | |
| "confidence": 1.0, | |
| "start_index": 526 | |
| }, | |
| { | |
| "text": "ููุงุฑููููุ", | |
| "confidence": 1.0, | |
| "start_index": 531 | |
| }, | |
| { | |
| "text": "ุฃูููุจูุฃู", | |
| "confidence": 1.0, | |
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| }, | |
| { | |
| "text": "ุงููุฌูุฑูููุฑููููุ", | |
| "confidence": 1.0, | |
| "start_index": 550 | |
| }, | |
| { | |
| "text": "ุนููู", | |
| "confidence": 1.0, | |
| "start_index": 566 | |
| }, | |
| { | |
| "text": "ุฃูุจูู", | |
| "confidence": 1.0, | |
| "start_index": 571 | |
| }, | |
| { | |
| "text": "ุงููุนูููุงุกูุ", | |
| "confidence": 1.0, | |
| "start_index": 577 | |
| }, | |
| { | |
| "text": "ุนููู", | |
| "confidence": 1.0, | |
| "start_index": 589 | |
| }, | |
| { | |
| "text": "ุนูุซูู ูุงูู", | |
| "confidence": 1.0, | |
| "start_index": 594 | |
| }, | |
| { | |
| "text": "ุจููู", | |
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| }, | |
| { | |
| "text": "ุฃูุจูู", | |
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| }, | |
| { | |
| "text": "ุงููุนูุงุตูุ", | |
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| { | |
| "text": "\\int_{3}^{M}", | |
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| "text": "=", | |
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| }, | |
| { | |
| "text": "\\theta^2", | |
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| }, | |
| { | |
| "text": "\\approx", | |
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| { | |
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| "start_index": 679 | |
| }, | |
| { | |
| "text": "##", | |
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| "start_index": 681 | |
| }, | |
| { | |
| "text": "ุจุฑูุงู", | |
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| "start_index": 684 | |
| }, | |
| { | |
| "text": "ุฑุถู", | |
| "confidence": 1.0, | |
| "start_index": 690 | |
| }, | |
| { | |
| "text": "ุงููู", | |
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| "start_index": 694 | |
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| { | |
| "text": "ุนูู", | |
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| }, | |
| { | |
| "text": "ููุงูู:", | |
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| }, | |
| { | |
| "text": "ููููุชู:", | |
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| }, | |
| { | |
| "text": "ููุง", | |
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| }, | |
| { | |
| "text": "ุฑูุณูููู", | |
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| "start_index": 722 | |
| }, | |
| { | |
| "text": "ุงูููููู", | |
| "confidence": 1.0, | |
| "start_index": 730 | |
| }, | |
| { | |
| "text": "ุฅูููู", | |
| "confidence": 1.0, | |
| "start_index": 738 | |
| }, | |
| { | |
| "text": "ุงูุดููููุทูุงูู", | |
| "confidence": 1.0, | |
| "start_index": 744 | |
| }, | |
| { | |
| "text": "ููุฏู", | |
| "confidence": 1.0, | |
| "start_index": 757 | |
| }, | |
| { | |
| "text": "ุญูุงูู", | |
| "confidence": 1.0, | |
| "start_index": 762 | |
| }, | |
| { | |
| "text": "ุจูููููู", | |
| "confidence": 1.0, | |
| "start_index": 768 | |
| }, | |
| { | |
| "text": "ููุจููููู", | |
| "confidence": 1.0, | |
| "start_index": 776 | |
| }, | |
| { | |
| "text": "ุตูููุงุชูู", | |
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| "start_index": 785 | |
| }, | |
| { | |
| "text": "ููููุฑูุงุกูุชูู", | |
| "confidence": 1.0, | |
| "start_index": 794 | |
| }, | |
| { | |
| "text": "ููููุงูู:", | |
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| "start_index": 807 | |
| }, | |
| { | |
| "text": "ยซุฅูููู", | |
| "confidence": 1.0, | |
| "start_index": 816 | |
| }, | |
| { | |
| "text": "ุฐููููู", | |
| "confidence": 1.0, | |
| "start_index": 823 | |
| }, | |
| { | |
| "text": "ุดูููุทูุงูู", | |
| "confidence": 1.0, | |
| "start_index": 830 | |
| }, | |
| { | |
| "text": "ููููุงูู", | |
| "confidence": 1.0, | |
| "start_index": 840 | |
| }, | |
| { | |
| "text": "ูููู", | |
| "confidence": 1.0, | |
| "start_index": 848 | |
| }, | |
| { | |
| "text": "ุฎูููุฒูุจู", | |
| "confidence": 1.0, | |
| "start_index": 853 | |
| }, | |
| { | |
| "text": "ููุฅูุฐูุง", | |
| "confidence": 1.0, | |
| "start_index": 862 | |
| }, | |
| { | |
| "text": "ุฃูุญูุณูุณูุชููู", | |
| "confidence": 1.0, | |
| "start_index": 870 | |
| }, | |
| { | |
| "text": "ููุชูุนููููุฐู", | |
| "confidence": 1.0, | |
| "start_index": 883 | |
| }, | |
| { | |
| "text": "ุจูุงูููููู", | |
| "confidence": 1.0, | |
| "start_index": 895 | |
| }, | |
| { | |
| "text": "ู ููููู", | |
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| "start_index": 905 | |
| }, | |
| { | |
| "text": "ููุงุชููููู", | |
| "confidence": 1.0, | |
| "start_index": 912 | |
| }, | |
| { | |
| "text": "ุนููู", | |
| "confidence": 1.0, | |
| "start_index": 922 | |
| }, | |
| { | |
| "text": "ููุณูุงุฑูููยป", | |
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| "start_index": 927 | |
| }, | |
| { | |
| "text": "ููุงูู:", | |
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| "start_index": 938 | |
| }, | |
| { | |
| "text": "ููููุนูููุชู", | |
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| "start_index": 945 | |
| }, | |
| { | |
| "text": "ููุฃูุฐูููุจู", | |
| "confidence": 1.0, | |
| "start_index": 956 | |
| }, | |
| { | |
| "text": "ุงูููููู", | |
| "confidence": 1.0, | |
| "start_index": 967 | |
| }, | |
| { | |
| "text": "ุนููููู", | |
| "confidence": 1.0, | |
| "start_index": 975 | |
| }, | |
| { | |
| "text": "ยซููุฐูุง", | |
| "confidence": 1.0, | |
| "start_index": 982 | |
| }, | |
| { | |
| "text": "ุญูุฏููุซู", | |
| "confidence": 1.0, | |
| "start_index": 989 | |
| }, | |
| { | |
| "text": "ุตูุญููุญู", | |
| "confidence": 1.0, | |
| "start_index": 997 | |
| }, | |
| { | |
| "text": "ุงููุฅูุณูููุงุฏู", | |
| "confidence": 1.0, | |
| "start_index": 1005 | |
| }, | |
| { | |
| "text": "ููููู ู", | |
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| "start_index": 1018 | |
| }, | |
| { | |
| "text": "\\iint_{D}", | |
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| { | |
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| { | |
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| { | |
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| { | |
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| { | |
| "text": "dx", | |
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| }, | |
| { | |
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| }, | |
| { | |
| "text": "dy", | |
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| "start_index": 1057 | |
| }, | |
| { | |
| "text": "##", | |
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| "start_index": 1060 | |
| }, | |
| { | |
| "text": "ุจุฑูุงู", | |
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| }, | |
| { | |
| "text": "ููุฎูุฑููุฌูุงููยป", | |
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| "text": "ุตุญูุญ", | |
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| { | |
| "text": "\\int_{3}^{M}", | |
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| { | |
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| { | |
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| { | |
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| { | |
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| { | |
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| }, | |
| { | |
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| { | |
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| }, | |
| { | |
| "text": "ุงูุฎูุงุฑ", | |
| "confidence": 1.0, | |
| "start_index": 1162 | |
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| { | |
| "text": "ู ู", | |
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| "start_index": 1169 | |
| }, | |
| { | |
| "text": "ุงูููุงุณุ", | |
| "confidence": 1.0, | |
| "start_index": 1172 | |
| }, | |
| { | |
| "text": "ูุงูุนูู", | |
| "confidence": 1.0, | |
| "start_index": 1180 | |
| }, | |
| { | |
| "text": "ุงูุฌุงุณูุณ.", | |
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| "start_index": 1187 | |
| }, | |
| { | |
| "text": "ูู ูุงุฏ", | |
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| "start_index": 1196 | |
| }, | |
| { | |
| "text": "ุงููุงุนุฏุฉ:", | |
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| }, | |
| { | |
| "text": "ุฃูู", | |
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| }, | |
| { | |
| "text": "ุงูู ุดุชุฑู", | |
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| "start_index": 1215 | |
| }, | |
| { | |
| "text": "ู ู", | |
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| }, | |
| { | |
| "text": "ุญูุซ", | |
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| "start_index": 1226 | |
| }, | |
| { | |
| "text": "ุญู ูู", | |
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| "start_index": 1230 | |
| }, | |
| { | |
| "text": "ุนูู", | |
| "confidence": 1.0, | |
| "start_index": 1235 | |
| }, | |
| { | |
| "text": "ููู", | |
| "confidence": 1.0, | |
| "start_index": 1239 | |
| }, | |
| { | |
| "text": "ู ุนุงููู", | |
| "confidence": 1.0, | |
| "start_index": 1243 | |
| }, | |
| { | |
| "text": "ุฃู", | |
| "confidence": 1.0, | |
| "start_index": 1250 | |
| }, | |
| { | |
| "text": "ุนูู", | |
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| "start_index": 1253 | |
| }, | |
| { | |
| "text": "ู ุนูู", | |
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| }, | |
| { | |
| "text": "ุฏูู", | |
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| }, | |
| { | |
| "text": "ุขุฎุฑ", | |
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| }, | |
| { | |
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| { | |
| "text": "ุฎูุงูููุฉ", | |
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| { | |
| "text": "\\sum_{\\alpha=0}^{100}", | |
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| }, | |
| { | |
| "text": "\\frac{z^\\alpha}{\\alpha!}", | |
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| { | |
| "text": "=", | |
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| { | |
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| { | |
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| { | |
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| { | |
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| "content": "ููุฎูุฑููุฌูุงููยป 7514 - ุตุญูุญ", | |
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| "content": "ูุงูุนูู ุงูุฎูุงุฑ ู ู ุงูููุงุณุ ูุงูุนูู ุงูุฌุงุณูุณ. ูู ูุงุฏ ุงููุงุนุฏุฉ: ุฃูู ุงูู ุดุชุฑู ู ู ุญูุซ ุญู ูู ุนูู ููู ู ุนุงููู ุฃู ุนูู ู ุนูู ุฏูู ุขุฎุฑ ู ุณุฃูุฉ ุฎูุงูููุฉ", | |
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| "content": "\\sum_{\\alpha=0}^{100} \\frac{z^\\alpha}{\\alpha!} = e^{z}", | |
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