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+{"segments": [{"id": 1, "seek": 1216, "start": 10.02, "end": 12.16, "text": "بسم الله الرحمن الرحيم", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640], "avg_logprob": -0.06440429762005806, "compression_ratio": 1.0789473684210527, "no_speech_prob": 0.0, "words": [{"start": 10.02, "end": 10.98, "word": "بسم", "probability": 0.80615234375}, {"start": 10.98, "end": 11.2, "word": " الله", "probability": 0.97998046875}, {"start": 11.2, "end": 11.66, "word": " الرحمن", "probability": 0.96240234375}, {"start": 11.66, "end": 12.16, "word": " الرحيم", "probability": 0.9943033854166666}], "temperature": 1.0}, {"id": 2, "seek": 3204, "start": 13.13, "end": 32.05, "text": "مواصل ما ابتدأنا به في المرة الماضية و هو موضوع ال power series طبعا ابتدينا فيه المرة الماضية و أخدنا على ذلك أربعة أمثلة و بنعطي الآن مثال بشكل آخر غير الأشكال الأربع اللي شفناها في المرة الماضية", "tokens": [2304, 2407, 33546, 1211, 19446, 48127, 2655, 3215, 10721, 8315, 39627, 8978, 9673, 25720, 9673, 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التلاتة المشهورة اللي كنا بنتعامل معاها طيلة هذا ال chapter بالمرة النهائية", "tokens": [3555, 1863, 3555, 4587, 7578, 9673, 33599, 1829, 5296, 17082, 995, 10632, 19446, 8717, 2407, 36520, 5296, 1783, 6055, 2288, 21292, 3615, 30767, 16373, 3215, 36764, 24401, 15844, 6055, 1211, 9307, 3660, 28242, 3224, 281, 264, 1347, 426, 30767, 16373, 3215, 30731, 19753, 34740, 9957, 7251, 3555, 4587, 7578, 9122, 2655, 3555, 8315, 2423, 2638, 15844, 25124, 28820, 13672, 1829, 12174, 3215, 10943, 8315, 21136, 33604, 6027, 31439, 8032, 3215, 2423, 2638, 8032, 1211, 39896, 9154, 2423, 2638, 16712, 1211, 9307, 3660, 9673, 8592, 3224, 13063, 3660, 13672, 1829, 9122, 8315, 44945, 2655, 3615, 10943, 1211, 20449, 995, 11296, 23032, 26895, 3660, 23758, 2423, 7187, 20666, 2304, 25720, 28239, 3224, 16373, 10632], "avg_logprob": -0.2206858407079646, "compression_ratio": 1.7854077253218885, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 82.74, "end": 83.58, "word": "بنبقى", "probability": 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"probability": 0.75048828125}, {"start": 1147.73, "end": 1148.43, "word": " X", "probability": 0.9375}, {"start": 1148.43, "end": 1149.65, "word": " بده", "probability": 0.4910888671875}, {"start": 1149.65, "end": 1150.19, "word": " تسوي", "probability": 0.7623697916666666}, {"start": 1150.19, "end": 1150.39, "word": " ال", "probability": 0.5751953125}, {"start": 1150.39, "end": 1151.07, "word": " summation", "probability": 0.744140625}, {"start": 1151.07, "end": 1151.53, "word": " من", "probability": 0.99072265625}, {"start": 1151.53, "end": 1151.85, "word": " N", "probability": 0.72509765625}, {"start": 1151.85, "end": 1152.35, "word": " equal", "probability": 0.61181640625}, {"start": 1152.35, "end": 1152.87, "word": " zero", "probability": 0.58154296875}, {"start": 1152.87, "end": 1153.17, "word": " to", "probability": 0.9658203125}, {"start": 1153.17, "end": 1154.03, "word": " infinity", "probability": 0.83251953125}, {"start": 1154.03, "end": 1155.11, "word": " ل", "probability": 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{"start": 1162.87, "end": 1164.35, "word": " X", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 48, "seek": 117827, "start": 1165.61, "end": 1178.27, "text": "اللي هي أكبر من ال A ناقص ال R وأقل من ال A زائد ال R وال R greater than zero", "tokens": [6027, 20292, 39896, 5551, 4117, 26890, 9154, 2423, 316, 8717, 995, 4587, 9381, 2423, 497, 36725, 4587, 1211, 9154, 2423, 316, 30767, 16373, 3215, 2423, 497, 16070, 497, 5044, 813, 4018], "avg_logprob": -0.2988281287252903, "compression_ratio": 1.2666666666666666, "no_speech_prob": 0.0, "words": [{"start": 1165.61, "end": 1166.11, "word": "اللي", "probability": 0.3880615234375}, {"start": 1166.11, "end": 1166.47, "word": " هي", "probability": 0.85986328125}, {"start": 1166.47, "end": 1167.25, "word": " أكبر", "probability": 0.85986328125}, {"start": 1167.25, "end": 1167.63, "word": " من", "probability": 0.99169921875}, {"start": 1167.63, "end": 1167.97, "word": " ال", "probability": 0.7861328125}, {"start": 1167.97, "end": 1168.23, "word": " A", "probability": 0.2479248046875}, {"start": 1168.23, "end": 1168.97, "word": " ناقص", "probability": 0.877197265625}, {"start": 1168.97, "end": 1169.19, "word": " ال", "probability": 0.95849609375}, {"start": 1169.19, "end": 1169.49, "word": " R", "probability": 0.89892578125}, {"start": 1169.49, "end": 1170.51, "word": " وأقل", "probability": 0.8025716145833334}, {"start": 1170.51, "end": 1170.87, "word": " من", "probability": 0.99609375}, {"start": 1170.87, "end": 1171.21, "word": " ال", "probability": 0.662109375}, {"start": 1171.21, "end": 1171.59, "word": " A", "probability": 0.95654296875}, {"start": 1171.59, "end": 1172.39, "word": " زائد", "probability": 0.9124348958333334}, {"start": 1172.39, "end": 1172.65, "word": " ال", "probability": 0.927734375}, {"start": 1172.65, "end": 1173.11, "word": " R", "probability": 0.97802734375}, {"start": 1173.11, "end": 1175.41, "word": " وال", "probability": 0.6279296875}, {"start": 1175.41, "end": 1176.13, "word": " R", "probability": 0.5908203125}, {"start": 1176.13, "end": 1177.13, "word": " greater", "probability": 0.361083984375}, {"start": 1177.13, "end": 1177.77, "word": " than", "probability": 0.9404296875}, {"start": 1177.77, "end": 1178.27, "word": " zero", "probability": 0.441162109375}], "temperature": 1.0}, {"id": 49, "seek": 120701, "start": 1202.33, "end": 1207.01, "text": "النفس الفترة اللي عندنا هذه", "tokens": [6027, 1863, 36178, 27188, 2655, 25720, 13672, 1829, 43242, 8315, 29538], "avg_logprob": -0.5026041517655054, "compression_ratio": 0.9433962264150944, "no_speech_prob": 0.0, "words": [{"start": 1202.33, "end": 1203.73, "word": "النفس", "probability": 0.5405069986979166}, {"start": 1203.73, "end": 1205.13, "word": " الفترة", "probability": 0.9767252604166666}, {"start": 1205.13, "end": 1205.93, "word": " اللي", "probability": 0.6834716796875}, {"start": 1205.93, "end": 1206.49, "word": " عندنا", "probability": 0.897216796875}, {"start": 1206.49, "end": 1207.01, "word": " هذه", "probability": 0.57275390625}], "temperature": 1.0}, {"id": 50, "seek": 123267, "start": 1207.79, "end": 1232.67, "text": "الـ A ناقص الـ R إلى الـ A زائد R and وفي نفس الوقت تكامل لل F of X DX بدي ساوي اللي هو summation من N equal zero to infinity لمين؟ للـCN X ناقص الـ A", "tokens": [6027, 39184, 316, 8717, 995, 4587, 9381, 2423, 39184, 497, 30731, 2423, 39184, 316, 30767, 16373, 3215, 497, 293, 4032, 41185, 8717, 36178, 2423, 30543, 2655, 6055, 4117, 10943, 1211, 24976, 479, 295, 1783, 48817, 4724, 16254, 8608, 995, 45865, 13672, 1829, 31439, 28811, 9154, 426, 2681, 4018, 281, 13202, 32767, 9957, 22807, 24976, 39184, 34, 45, 1783, 8717, 995, 4587, 9381, 2423, 39184, 316], "avg_logprob": -0.29474432721282495, "compression_ratio": 1.3132530120481927, "no_speech_prob": 0.0, "words": [{"start": 1207.79, "end": 1208.37, "word": "الـ", "probability": 0.35345458984375}, {"start": 1208.37, "end": 1208.55, "word": " A", "probability": 0.25927734375}, {"start": 1208.55, "end": 1209.09, 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"probability": 0.82958984375}, {"start": 1224.59, "end": 1225.09, "word": " equal", "probability": 0.65087890625}, {"start": 1225.09, "end": 1225.57, "word": " zero", "probability": 0.51708984375}, {"start": 1225.57, "end": 1225.89, "word": " to", "probability": 0.97216796875}, {"start": 1225.89, "end": 1227.03, "word": " infinity", "probability": 0.8515625}, {"start": 1227.03, "end": 1228.53, "word": " لمين؟", "probability": 0.7139485677083334}, {"start": 1228.53, "end": 1229.83, "word": " للـCN", "probability": 0.4765625}, {"start": 1229.83, "end": 1230.69, "word": " X", "probability": 0.82080078125}, {"start": 1230.69, "end": 1231.69, "word": " ناقص", "probability": 0.9901123046875}, {"start": 1231.69, "end": 1232.29, "word": " الـ", "probability": 0.948974609375}, {"start": 1232.29, "end": 1232.67, "word": " A", "probability": 0.72021484375}], "temperature": 1.0}, {"id": 51, "seek": 125996, "start": 1233.24, "end": 1259.96, "text": "to the power n plus one على n plus one plus constant c على نفس الفترة اللي هو من a ناقص r إلى a زائد r examples consider the function", "tokens": [1353, 264, 1347, 297, 1804, 472, 15844, 297, 1804, 472, 1804, 5754, 269, 15844, 8717, 36178, 27188, 2655, 25720, 13672, 1829, 31439, 9154, 257, 8717, 995, 4587, 9381, 367, 30731, 257, 30767, 16373, 3215, 367, 5110, 1949, 264, 2445], "avg_logprob": -0.24707031548023223, "compression_ratio": 1.255639097744361, "no_speech_prob": 0.0, "words": [{"start": 1233.24, "end": 1233.5, "word": "to", "probability": 0.1444091796875}, {"start": 1233.5, "end": 1233.8, "word": " the", "probability": 0.8408203125}, {"start": 1233.8, "end": 1234.44, "word": " power", "probability": 0.90869140625}, {"start": 1234.44, "end": 1235.14, "word": " n", "probability": 0.427001953125}, {"start": 1235.14, "end": 1235.8, "word": " plus", "probability": 0.42919921875}, {"start": 1235.8, "end": 1236.38, "word": " one", "probability": 0.892578125}, {"start": 1236.38, "end": 1237.32, "word": " على", "probability": 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{"start": 1244.82, "end": 1245.26, "word": " a", "probability": 0.85595703125}, {"start": 1245.26, "end": 1245.96, "word": " ناقص", "probability": 0.944580078125}, {"start": 1245.96, "end": 1246.5, "word": " r", "probability": 0.414794921875}, {"start": 1246.5, "end": 1247.32, "word": " إلى", "probability": 0.79736328125}, {"start": 1247.32, "end": 1248.08, "word": " a", "probability": 0.96923828125}, {"start": 1248.08, "end": 1249.42, "word": " زائد", "probability": 0.8580729166666666}, {"start": 1249.42, "end": 1249.9, "word": " r", "probability": 0.71484375}, {"start": 1249.9, "end": 1253.22, "word": " examples", "probability": 0.348876953125}, {"start": 1253.22, "end": 1259.04, "word": " consider", "probability": 0.91650390625}, {"start": 1259.04, "end": 1259.34, "word": " the", "probability": 0.7177734375}, {"start": 1259.34, "end": 1259.96, "word": " function", "probability": 0.974609375}], "temperature": 1.0}, {"id": 52, "seek": 127338, "start": 1264.68, "end": 1273.38, "text": "يعتبر الدالة EO6 يساوي summation من N equal zero to infinity", "tokens": [1829, 34268, 26890, 32748, 6027, 3660, 462, 46, 21, 7251, 3794, 995, 45865, 28811, 9154, 426, 2681, 4018, 281, 13202], "avg_logprob": -0.48288691611517043, "compression_ratio": 0.9285714285714286, "no_speech_prob": 0.0, "words": [{"start": 1264.68, "end": 1265.44, "word": "يعتبر", "probability": 0.4962158203125}, {"start": 1265.44, "end": 1266.34, "word": " الدالة", "probability": 0.9148763020833334}, {"start": 1266.34, "end": 1268.12, "word": " EO6", "probability": 0.606689453125}, {"start": 1268.12, "end": 1268.84, "word": " يساوي", "probability": 0.73016357421875}, {"start": 1268.84, "end": 1269.8, "word": " summation", "probability": 0.126220703125}, {"start": 1269.8, "end": 1270.84, "word": " من", "probability": 0.8828125}, {"start": 1270.84, "end": 1271.2, "word": " N", "probability": 0.6298828125}, {"start": 1271.2, "end": 1271.7, "word": " equal", "probability": 0.157958984375}, {"start": 1271.7, "end": 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"word": " all", "probability": 0.9609375}, {"start": 1300.38, "end": 1301.04, "word": " x", "probability": 0.990234375}], "temperature": 1.0}, {"id": 54, "seek": 132983, "start": 1302.53, "end": 1329.83, "text": "المطلوب الأول show that بيّلي ان مشتقة ال EO6 بده تساوي ال EO6 نمرا بيه show that بيّلي تكامل ال EO6 DX بده يساوي ال EO6 زائد constant C", "tokens": [45340, 9566, 1211, 37746, 16247, 12610, 855, 300, 4724, 1829, 11703, 20292, 16472, 37893, 2655, 28671, 2423, 462, 46, 21, 47525, 3224, 6055, 3794, 995, 45865, 2423, 462, 46, 21, 8717, 2304, 23557, 4724, 1829, 3224, 855, 300, 4724, 1829, 11703, 20292, 6055, 4117, 10943, 1211, 2423, 462, 46, 21, 48817, 47525, 3224, 7251, 3794, 995, 45865, 2423, 462, 46, 21, 30767, 16373, 3215, 5754, 383], "avg_logprob": -0.2910447627750795, "compression_ratio": 1.4855072463768115, "no_speech_prob": 0.0, "words": [{"start": 1302.53, "end": 1303.21, "word": "المطلوب", "probability": 0.77392578125}, {"start": 1303.21, "end": 1303.97, "word": " الأول", "probability": 0.92431640625}, {"start": 1303.97, "end": 1304.93, "word": " show", "probability": 0.260498046875}, {"start": 1304.93, "end": 1305.73, "word": " that", "probability": 0.82373046875}, {"start": 1305.73, "end": 1307.87, "word": " بيّلي", "probability": 0.58697509765625}, {"start": 1307.87, "end": 1308.43, "word": " ان", "probability": 0.37060546875}, {"start": 1308.43, "end": 1310.55, "word": " مشتقة", "probability": 0.740478515625}, {"start": 1310.55, "end": 1311.77, "word": " ال", "probability": 0.744140625}, {"start": 1311.77, "end": 1312.89, "word": " EO6", "probability": 0.7157389322916666}, {"start": 1312.89, "end": 1313.77, "word": " بده", "probability": 0.2491455078125}, {"start": 1313.77, "end": 1314.29, "word": " تساوي", "probability": 0.9215087890625}, {"start": 1314.29, "end": 1314.49, "word": " ال", "probability": 0.78369140625}, {"start": 1314.49, "end": 1315.35, "word": " EO6", "probability": 0.9611002604166666}, {"start": 1315.35, "end": 1316.65, "word": " 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" بنتكلم", "probability": 0.808837890625}, {"start": 1359.91, "end": 1360.91, "word": " عن", "probability": 0.962890625}, {"start": 1360.91, "end": 1361.83, "word": " الاشتقاق", "probability": 0.744873046875}, {"start": 1361.83, "end": 1362.01, "word": " لل", "probability": 0.9453125}, {"start": 1362.01, "end": 1362.43, "word": " power", "probability": 0.5283203125}, {"start": 1362.43, "end": 1363.25, "word": " series", "probability": 0.87255859375}, {"start": 1363.25, "end": 1363.83, "word": " و", "probability": 0.5439453125}, {"start": 1363.83, "end": 1364.35, "word": " as", "probability": 0.798828125}, {"start": 1364.35, "end": 1364.75, "word": " a", "probability": 0.9521484375}, {"start": 1364.75, "end": 1365.29, "word": " function", "probability": 0.98046875}], "temperature": 1.0}, {"id": 56, "seek": 139353, "start": 1365.89, "end": 1393.53, "text": "محطوطة ال series اللي عندنا as a function على الشكل اللي عندنا هذا اشتقنا مرة و مرتين و في كل مرة بتغير ال index اللي تحت ال summation كل اشتقاق بنجس ال index بمقدار واحد ال series المشتقة و ال series الأصلية كلهم converge على نفس الفترة تعليل ال integration term by term", "tokens": [2304, 5016, 9566, 2407, 9566, 3660, 2423, 2638, 13672, 1829, 43242, 8315, 382, 257, 2445, 15844, 25124, 28820, 13672, 1829, 43242, 8315, 23758, 1975, 8592, 2655, 4587, 8315, 3714, 25720, 4032, 3714, 43500, 9957, 4032, 8978, 28242, 3714, 25720, 39894, 17082, 13546, 2423, 8186, 13672, 1829, 6055, 33753, 2423, 28811, 28242, 1975, 8592, 2655, 4587, 995, 4587, 44945, 7435, 3794, 2423, 8186, 4724, 2304, 28543, 9640, 36764, 24401, 2423, 2638, 9673, 8592, 2655, 28671, 4032, 2423, 2638, 16247, 9381, 1211, 10632, 28242, 16095, 41881, 15844, 8717, 36178, 27188, 2655, 25720, 37279, 20292, 1211, 2423, 10980, 1433, 538, 1433], "avg_logprob": -0.15482954906694818, "compression_ratio": 1.8114035087719298, "no_speech_prob": 0.0, "words": [{"start": 1365.89, "end": 1366.91, "word": "محطوطة", "probability": 0.7412109375}, {"start": 1366.91, "end": 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"word": " المشتقة", "probability": 0.9757080078125}, {"start": 1386.05, "end": 1386.45, "word": " و", "probability": 0.63134765625}, {"start": 1386.45, "end": 1386.55, "word": " ال", "probability": 0.80517578125}, {"start": 1386.55, "end": 1386.75, "word": " series", "probability": 0.8681640625}, {"start": 1386.75, "end": 1387.53, "word": " الأصلية", "probability": 0.73419189453125}, {"start": 1387.53, "end": 1388.11, "word": " كلهم", "probability": 0.955322265625}, {"start": 1388.11, "end": 1388.73, "word": " converge", "probability": 0.82568359375}, {"start": 1388.73, "end": 1389.05, "word": " على", "probability": 0.9013671875}, {"start": 1389.05, "end": 1389.47, "word": " نفس", "probability": 0.998046875}, {"start": 1389.47, "end": 1390.23, "word": " الفترة", "probability": 0.9939778645833334}, {"start": 1390.23, "end": 1391.35, "word": " تعليل", "probability": 0.6941731770833334}, {"start": 1391.35, "end": 1391.51, "word": " ال", "probability": 0.99365234375}, {"start": 1391.51, "end": 1392.07, "word": " integration", "probability": 0.9775390625}, {"start": 1392.07, "end": 1392.57, "word": " term", "probability": 0.72509765625}, {"start": 1392.57, "end": 1392.91, "word": " by", "probability": 0.96728515625}, {"start": 1392.91, "end": 1393.53, "word": " term", "probability": 0.95654296875}], "temperature": 1.0}, {"id": 57, "seek": 141123, "start": 1394.01, "end": 1411.23, "text": "يعني بدنا نكامل كل term من حدود ال series ونعرف ما هو شكل ال series الناتجة يفترض ان ال F of X مكتوبة عندي على شكل summation بهذا الشكل طبعا يمكن تستغربوا", "tokens": [40228, 22653, 47525, 8315, 8717, 4117, 10943, 1211, 28242, 1433, 9154, 11331, 3215, 23328, 2423, 2638, 4032, 1863, 3615, 28480, 19446, 31439, 13412, 28820, 2423, 2638, 28239, 9307, 7435, 3660, 7251, 5172, 2655, 43042, 16472, 2423, 479, 295, 1783, 3714, 4117, 2655, 37746, 3660, 18871, 16254, 15844, 13412, 28820, 28811, 39627, 15730, 25124, 28820, 23032, 3555, 3615, 995, 7251, 43020, 6055, 14851, 17082, 25513, 14407], 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"probability": 0.9095703125}, {"start": 1405.87, "end": 1406.23, "word": " عندي", "probability": 0.7303466796875}, {"start": 1406.23, "end": 1406.55, "word": " على", "probability": 0.91650390625}, {"start": 1406.55, "end": 1407.11, "word": " شكل", "probability": 0.9814453125}, {"start": 1407.11, "end": 1407.79, "word": " summation", "probability": 0.80810546875}, {"start": 1407.79, "end": 1408.43, "word": " بهذا", "probability": 0.945556640625}, {"start": 1408.43, "end": 1408.93, "word": " الشكل", "probability": 0.99169921875}, {"start": 1408.93, "end": 1409.93, "word": " طبعا", "probability": 0.9315185546875}, {"start": 1409.93, "end": 1410.19, "word": " يمكن", "probability": 0.957763671875}, {"start": 1410.19, "end": 1411.23, "word": " تستغربوا", "probability": 0.9322265625}], "temperature": 1.0}, {"id": 58, "seek": 143384, "start": 1411.46, "end": 1433.84, "text": "ان ال function مكتوبة على شكل summation بهذا الشكل ولا استغرب ولا حاجة المحاضرة القادمة ان شاء الله يعني ال section 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constant وعلى نفس ال interval اللي عندنا", "tokens": [3615, 10943, 1211, 8315, 5296, 11296, 6055, 4117, 10943, 1211, 9122, 33456, 3224, 9122, 10943, 1211, 8315, 11296, 7251, 3555, 4587, 7578, 2423, 2638, 8032, 8848, 1829, 41881, 15844, 8717, 36178, 27188, 2655, 25720, 46599, 6027, 2655, 6027, 1829, 6055, 4117, 10943, 1211, 24976, 283, 295, 2031, 30017, 7251, 3794, 2407, 7578, 28239, 31371, 7435, 3660, 13672, 1829, 43242, 8315, 8032, 8848, 1829, 20666, 11242, 3555, 9566, 46811, 10943, 995, 30767, 18513, 587, 30767, 18513, 5754, 4032, 3615, 23942, 8717, 36178, 2423, 15035, 13672, 1829, 43242, 8315], "avg_logprob": -0.216974426060915, "compression_ratio": 1.7027027027027026, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1459.57, "end": 1460.35, "word": "عاملنا", "probability": 0.5827484130859375}, {"start": 1460.35, "end": 1460.57, "word": " لها", "probability": 0.856201171875}, {"start": 1460.57, "end": 1461.53, "word": " تكامل", "probability": 0.9803466796875}, {"start": 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integration term by term سواء جلي او مجليش يعني مجليش استخدم ال differentiation او استخدم ال integration او اطالي مثلا و بده حلة", "tokens": [3555, 1863, 47283, 3215, 5551, 2304, 12984, 37977, 15844, 2423, 38902, 1433, 538, 1433, 4032, 2423, 10980, 1433, 538, 1433, 8608, 2407, 16606, 10874, 20292, 1975, 2407, 3714, 7435, 20292, 8592, 37495, 22653, 3714, 7435, 20292, 8592, 44713, 9778, 40448, 2423, 38902, 1975, 2407, 44713, 9778, 40448, 2423, 10980, 1975, 2407, 1975, 9566, 6027, 1829, 50113, 15040, 4032, 47525, 3224, 11331, 1211, 3660], "avg_logprob": -0.3242187453433871, "compression_ratio": 1.7315436241610738, "no_speech_prob": 0.0, "words": [{"start": 1482.0600000000002, "end": 1482.8600000000001, "word": "بناخد", "probability": 0.56134033203125}, {"start": 1482.8600000000001, "end": 1483.66, "word": " أمثلة", "probability": 0.8671875}, {"start": 1483.66, "end": 1484.18, "word": " على", "probability": 0.6435546875}, {"start": 1484.18, "end": 1484.58, "word": " ال", "probability": 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"end": 1512.09, "word": " ال", "probability": 0.9189453125}, {"start": 1512.09, "end": 1512.61, "word": " interval", "probability": 0.87255859375}, {"start": 1512.61, "end": 1513.07, "word": " of", "probability": 0.9619140625}, {"start": 1513.07, "end": 1513.85, "word": " convergence", "probability": 0.966796875}], "temperature": 1.0}, {"id": 63, "seek": 153443, "start": 1514.31, "end": 1534.43, "text": "من سالب infinity إلى infinity واحنا شوفنا في ال power series ممكن تكون ال series converge على كل ال real line بلا ستة نار المطلوب الأول بيقول إن مشتقة ال EO6 هي ال EO6 itself طب هذا خدناه أين؟", "tokens": [27842, 8608, 6027, 3555, 13202, 30731, 13202, 4032, 39319, 8315, 13412, 38688, 8315, 8978, 2423, 1347, 2638, 3714, 43020, 6055, 30544, 2423, 2638, 41881, 15844, 28242, 2423, 957, 1622, 4724, 15040, 8608, 2655, 3660, 8717, 9640, 9673, 9566, 1211, 37746, 16247, 12610, 4724, 1829, 39648, 36145, 37893, 2655, 28671, 2423, 462, 46, 21, 39896, 2423, 462, 46, 21, 2564, 23032, 3555, 23758, 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"end": 1525.39, "word": " ستة", "probability": 0.7198079427083334}, {"start": 1525.39, "end": 1525.75, "word": " نار", "probability": 0.48138427734375}, {"start": 1525.75, "end": 1526.81, "word": " المطلوب", "probability": 0.8651123046875}, {"start": 1526.81, "end": 1527.23, "word": " الأول", "probability": 0.930908203125}, {"start": 1527.23, "end": 1527.63, "word": " بيقول", "probability": 0.6571451822916666}, {"start": 1527.63, "end": 1527.85, "word": " إن", "probability": 0.283935546875}, {"start": 1527.85, "end": 1528.63, "word": " مشتقة", "probability": 0.9210611979166666}, {"start": 1528.63, "end": 1528.89, "word": " ال", "probability": 0.9658203125}, {"start": 1528.89, "end": 1529.67, "word": " EO6", "probability": 0.7210286458333334}, {"start": 1529.67, "end": 1530.13, "word": " هي", "probability": 0.9365234375}, {"start": 1530.13, "end": 1530.75, "word": " ال", "probability": 0.8974609375}, {"start": 1530.75, "end": 1531.55, "word": " EO6", "probability": 0.92919921875}, 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تلاتة في اتنين factorial هذه N في N ناقص واحد factorial", "tokens": [9566, 1829, 3555, 46811, 10943, 7251, 3555, 4587, 7578, 20328, 9640, 18871, 16254, 413, 15844, 48817, 24976, 462, 46, 21, 7251, 3794, 995, 45865, 36764, 24401, 30767, 16373, 2288, 29538, 45164, 6156, 4117, 36081, 11296, 6225, 3555, 9640, 3660, 18871, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 8978, 36764, 24401, 36916, 29538, 6055, 1211, 9307, 3660, 8978, 1975, 2655, 1863, 9957, 36916, 29538, 426, 8978, 426, 8717, 995, 4587, 9381, 36764, 24401, 36916], "avg_logprob": -0.21484375098033956, "compression_ratio": 1.6981132075471699, "no_speech_prob": 0.0, "words": [{"start": 1607.56, "end": 1608.06, "word": "طيب", "probability": 0.7596842447916666}, {"start": 1608.06, "end": 1608.6, "word": " تمام", "probability": 0.97021484375}, {"start": 1608.6, "end": 1609.04, "word": " يبقى", "probability": 0.9381103515625}, {"start": 1609.04, "end": 1609.62, "word": " صار", "probability": 0.6885986328125}, {"start": 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"word": " زائد", "probability": 0.9767252604166666}, {"start": 1652.66, "end": 1653.66, "word": " زائد", "probability": 0.9602864583333334}], "temperature": 1.0}, {"id": 69, "seek": 167019, "start": 1654.73, "end": 1670.19, "text": "بتروح ال N مع ال N يبقى X أس N minus ال one N minus ال one factorial بالشكل اللي عندنا هنا زائد إلى آخرين", "tokens": [3555, 2655, 32887, 5016, 2423, 426, 20449, 2423, 426, 7251, 3555, 4587, 7578, 1783, 5551, 3794, 426, 3175, 2423, 472, 426, 3175, 2423, 472, 36916, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 34105, 30767, 16373, 3215, 30731, 19753, 34740, 9957], "avg_logprob": -0.2576219454044249, "compression_ratio": 1.2580645161290323, "no_speech_prob": 0.0, "words": [{"start": 1654.73, "end": 1655.45, "word": "بتروح", "probability": 0.7626953125}, {"start": 1655.45, "end": 1655.67, "word": " ال", "probability": 0.9169921875}, {"start": 1655.67, "end": 1655.97, "word": " N", "probability": 0.432373046875}, {"start": 1655.97, "end": 1656.25, "word": " 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عندنا هذا طب ال index اللي تحت ال summation من وين بده يبدأ؟", "tokens": [1829, 3555, 4587, 7578, 2423, 7649, 39894, 32887, 5016, 1975, 4117, 2655, 3555, 11296, 15844, 13412, 28820, 28811, 7251, 3555, 4587, 7578, 45164, 9122, 2655, 3555, 2655, 11296, 15844, 13412, 28820, 28811, 47525, 3224, 5551, 9381, 13546, 28811, 24976, 24401, 16472, 3224, 22653, 2031, 5551, 10859, 3794, 297, 12, 16, 15844, 297, 12, 16, 36916, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23758, 23032, 3555, 2423, 8186, 13672, 1829, 6055, 33753, 2423, 28811, 9154, 4032, 9957, 47525, 3224, 7251, 44510, 10721, 22807], "avg_logprob": -0.2628012191818421, "compression_ratio": 1.638743455497382, "no_speech_prob": 0.0, "words": [{"start": 1671.01, "end": 1671.47, "word": "يبقى", "probability": 0.682952880859375}, {"start": 1671.47, "end": 1671.75, "word": " الان", "probability": 0.6517333984375}, {"start": 1671.75, "end": 1672.19, "word": " بتروح", "probability": 0.7217610677083334}, {"start": 1672.19, "end": 1672.73, 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واحد على واحد بواحد اللي هو الحد الاول زاد وضع ن بواحد بيجيب الحد التاني و الحد التالت والربع يبقى بالكلام سليم مائة بالمائة", "tokens": [1829, 39648, 4117, 3714, 33599, 1829, 3714, 9381, 3215, 4587, 10874, 25513, 4032, 11242, 3615, 8717, 4724, 11622, 13546, 2407, 6156, 995, 4117, 2655, 13063, 25528, 13672, 1829, 4724, 1829, 7435, 1829, 11778, 33599, 2288, 4724, 14407, 24401, 34105, 1783, 4032, 17182, 4724, 14407, 24401, 7251, 3555, 4587, 7578, 36764, 24401, 15844, 36764, 24401, 4724, 14407, 24401, 13672, 1829, 31439, 21542, 3215, 42963, 12610, 30767, 18513, 4032, 11242, 3615, 8717, 4724, 14407, 24401, 4724, 1829, 7435, 1829, 3555, 21542, 3215, 16712, 7649, 1829, 4032, 21542, 3215, 16712, 6027, 2655, 16070, 25513, 3615, 7251, 3555, 4587, 7578, 20666, 28820, 10943, 8608, 20292, 2304, 3714, 16373, 3660, 20666, 2304, 16373, 3660], "avg_logprob": -0.36761365072293717, "compression_ratio": 2.032608695652174, "no_speech_prob": 0.0, "words": [{"start": 2181.77, "end": 2182.17, "word": 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2327.77, "end": 2328.51, "word": " sub", "probability": 0.537109375}, {"start": 2328.51, "end": 2328.75, "word": " machine", "probability": 0.8115234375}, {"start": 2328.75, "end": 2329.01, "word": " هو", "probability": 0.457763671875}, {"start": 2329.01, "end": 2329.15, "word": " ال", "probability": 0.8505859375}, {"start": 2329.15, "end": 2329.61, "word": " exponential", "probability": 0.91845703125}, {"start": 2329.61, "end": 2330.39, "word": " function", "probability": 0.97216796875}, {"start": 2330.39, "end": 2331.05, "word": " وده", "probability": 0.6365559895833334}, {"start": 2331.05, "end": 2331.23, "word": " ال", "probability": 0.90673828125}, {"start": 2331.23, "end": 2331.71, "word": " constant", "probability": 0.94482421875}, {"start": 2331.71, "end": 2332.11, "word": " يبقى", "probability": 0.95458984375}, {"start": 2332.11, "end": 2332.53, "word": " فعلا", "probability": 0.9288736979166666}, {"start": 2332.53, "end": 2333.17, "word": " تكمل", "probability": 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مثال", "probability": 0.949462890625}, {"start": 2340.61, "end": 2340.87, "word": " على", "probability": 0.9072265625}, {"start": 2340.87, "end": 2341.23, "word": " هذا", "probability": 0.97119140625}, {"start": 2341.23, "end": 2341.85, "word": " الموضوع", "probability": 0.9981689453125}, {"start": 2341.85, "end": 2342.83, "word": " وفتح", "probability": 0.8201904296875}, {"start": 2342.83, "end": 2343.21, "word": " عينك", "probability": 0.9767252604166666}, {"start": 2343.21, "end": 2343.73, "word": " كويس", "probability": 0.94873046875}, {"start": 2343.73, "end": 2344.19, "word": " دجج", "probability": 0.6646728515625}, {"start": 2344.19, "end": 2344.61, "word": " معايا", "probability": 0.8269856770833334}], "temperature": 1.0}, {"id": 96, "seek": 237169, "start": 2345.27, "end": 2371.69, "text": "مثال رقم اتنين بيقول find a function f of x that represented by", "tokens": [2304, 12984, 6027, 12602, 4587, 2304, 1975, 2655, 1863, 9957, 4724, 1829, 39648, 915, 257, 2445, 283, 295, 2031, 300, 10379, 538], "avg_logprob": -0.26800271479979804, "compression_ratio": 0.9411764705882353, "no_speech_prob": 0.0, "words": [{"start": 2345.27, "end": 2345.83, "word": "مثال", "probability": 0.8977864583333334}, {"start": 2345.83, "end": 2346.39, "word": " رقم", "probability": 0.8816731770833334}, {"start": 2346.39, "end": 2347.01, "word": " اتنين", "probability": 0.9112548828125}, {"start": 2347.01, "end": 2355.57, "word": " بيقول", "probability": 0.6053263346354166}, {"start": 2355.57, "end": 2356.13, "word": " find", "probability": 0.623046875}, {"start": 2356.13, "end": 2356.53, "word": " a", "probability": 0.96142578125}, {"start": 2356.53, "end": 2360.95, "word": " function", "probability": 0.98095703125}, {"start": 2360.95, "end": 2362.05, "word": " f", "probability": 0.634765625}, {"start": 2362.05, "end": 2362.57, "word": " of", "probability": 0.54931640625}, {"start": 2362.57, "end": 2363.25, "word": " x", "probability": 0.9404296875}, {"start": 2363.25, "end": 2364.29, "word": " that", "probability": 0.900390625}, {"start": 2364.29, "end": 2369.73, "word": " represented", "probability": 0.728515625}, {"start": 2369.73, "end": 2371.69, "word": " by", "probability": 0.88671875}], "temperature": 1.0}, {"id": 97, "seek": 239661, "start": 2377.51, "end": 2396.61, "text": "بعد عملية عملية عملية عملية عملية عملية عملية عملية عملية عملية عملية عملية", "tokens": [3555, 22488, 6225, 42213, 10632, 6225, 42213, 10632, 6225, 42213, 10632, 6225, 42213, 10632, 6225, 42213, 10632, 6225, 42213, 10632, 6225, 42213, 10632, 6225, 42213, 10632, 6225, 42213, 10632, 6225, 42213, 10632, 6225, 42213, 10632, 6225, 42213, 10632], "avg_logprob": -0.520432710647583, "compression_ratio": 4.758620689655173, "no_speech_prob": 0.0, "words": [{"start": 2377.5099999999998, "end": 2378.91, "word": "بعد", "probability": 0.22796630859375}, {"start": 2378.91, "end": 2379.31, "word": " عملية", "probability": 0.3291829427083333}, {"start": 2379.31, "end": 2379.31, "word": " عملية", "probability": 0.7368977864583334}, {"start": 2379.31, "end": 2380.11, "word": " عملية", "probability": 0.778076171875}, {"start": 2380.11, "end": 2380.25, "word": " عملية", "probability": 0.7764485677083334}, {"start": 2380.25, "end": 2380.25, "word": " عملية", "probability": 0.7560221354166666}, {"start": 2380.25, "end": 2380.25, "word": " عملية", "probability": 0.7327473958333334}, {"start": 2380.25, "end": 2381.97, "word": " عملية", "probability": 0.7574869791666666}, {"start": 2381.97, "end": 2382.61, "word": " عملية", "probability": 0.8094075520833334}, {"start": 2382.61, "end": 2382.93, "word": " عملية", "probability": 0.8693033854166666}, {"start": 2382.93, "end": 2384.73, "word": " عملية", "probability": 0.9085286458333334}, {"start": 2384.73, "end": 2385.97, "word": " عملية", "probability": 0.9352213541666666}, {"start": 2385.97, "end": 2396.61, "word": " عملية", "probability": 0.9514973958333334}], "temperature": 1.0}, {"id": 98, "seek": 242778, "start": 2399.32, "end": 2427.78, "text": "the result استخدم النتيجة اللي حصلت عليها to find a power series that represent that represent that represent the following", "tokens": [3322, 1874, 44713, 9778, 40448, 28239, 31371, 7435, 3660, 13672, 1829, 11331, 36520, 2655, 25894, 11296, 281, 915, 257, 1347, 2638, 300, 2906, 300, 2906, 300, 2906, 264, 3480], "avg_logprob": -0.23736978868643444, "compression_ratio": 1.3303571428571428, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2399.32, "end": 2399.76, "word": "the", "probability": 0.118408203125}, {"start": 2399.76, "end": 2400.88, "word": " result", "probability": 0.9677734375}, {"start": 2400.88, "end": 2402.28, "word": " استخدم", "probability": 0.8873697916666666}, {"start": 2402.28, "end": 2402.96, "word": " النتيجة", "probability": 0.9781494140625}, {"start": 2402.96, "end": 2403.12, "word": " اللي", "probability": 0.756103515625}, {"start": 2403.12, "end": 2403.76, "word": " حصلت", "probability": 0.9879557291666666}, {"start": 2403.76, 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2427.02, "word": " the", "probability": 0.80419921875}, {"start": 2427.02, "end": 2427.78, "word": " following", "probability": 0.9013671875}], "temperature": 1.0}, {"id": 99, "seek": 245666, "start": 2433.02, "end": 2456.66, "text": "التي تمثل الدوالة التالية الدالة الأولى نمره A الـG of X يساوي واحد على واحد زائد X لكل تربية نمره B الـG of X بده يساوي Len واحد زائد X", "tokens": [6027, 31371, 46811, 12984, 1211, 32748, 2407, 6027, 3660, 16712, 6027, 10632, 32748, 6027, 3660, 16247, 12610, 7578, 8717, 29973, 3224, 316, 2423, 39184, 38, 295, 1783, 7251, 3794, 995, 45865, 36764, 24401, 15844, 36764, 24401, 30767, 16373, 3215, 1783, 5296, 28820, 6055, 25513, 10632, 8717, 29973, 3224, 363, 2423, 39184, 38, 295, 1783, 47525, 3224, 7251, 3794, 995, 45865, 23009, 36764, 24401, 30767, 16373, 3215, 1783], "avg_logprob": -0.29090074581258435, "compression_ratio": 1.6888888888888889, "no_speech_prob": 0.0, "words": [{"start": 2433.02, "end": 2434.36, "word": "التي", "probability": 0.1478271484375}, {"start": 2434.36, "end": 2435.08, "word": " تمثل", "probability": 0.9339192708333334}, {"start": 2435.08, "end": 2435.94, "word": " الدوالة", "probability": 0.7254638671875}, {"start": 2435.94, "end": 2436.58, "word": " التالية", "probability": 0.8263346354166666}, {"start": 2436.58, "end": 2437.9, "word": " الدالة", "probability": 0.8758138020833334}, {"start": 2437.9, "end": 2438.44, "word": " الأولى", "probability": 0.9552408854166666}, {"start": 2438.44, "end": 2439.08, "word": " نمره", "probability": 0.4696858723958333}, {"start": 2439.08, "end": 2439.52, "word": " A", "probability": 0.389892578125}, {"start": 2439.52, "end": 2440.78, "word": " الـG", "probability": 0.4715983072916667}, {"start": 2440.78, "end": 2441.24, "word": " of", "probability": 0.60888671875}, {"start": 2441.24, "end": 2441.84, "word": " X", "probability": 0.9619140625}, {"start": 2441.84, "end": 2443.18, "word": " يساوي", "probability": 0.7933349609375}, {"start": 2443.18, "end": 2443.86, "word": " واحد", "probability": 0.87158203125}, {"start": 2443.86, "end": 2444.14, "word": " على", "probability": 0.5576171875}, {"start": 2444.14, "end": 2444.68, "word": " واحد", "probability": 0.984375}, {"start": 2444.68, "end": 2445.26, "word": " زائد", "probability": 0.9344075520833334}, {"start": 2445.26, "end": 2445.66, "word": " X", "probability": 0.97705078125}, {"start": 2445.66, "end": 2446.32, "word": " لكل", "probability": 0.927978515625}, {"start": 2446.32, "end": 2447.12, "word": " تربية", "probability": 0.6946614583333334}, {"start": 2447.12, "end": 2448.52, "word": " نمره", "probability": 0.8531901041666666}, {"start": 2448.52, "end": 2448.88, "word": " B", "probability": 0.87109375}, {"start": 2448.88, "end": 2450.08, "word": " الـG", "probability": 0.8406575520833334}, {"start": 2450.08, "end": 2450.6, "word": " of", "probability": 0.95849609375}, {"start": 2450.6, "end": 2451.18, "word": " X", "probability": 0.99658203125}, {"start": 2451.18, "end": 2452.04, "word": " بده", "probability": 0.693603515625}, {"start": 2452.04, "end": 2452.92, "word": " يساوي", "probability": 0.9764404296875}, {"start": 2452.92, "end": 2454.14, "word": " Len", "probability": 0.2420654296875}, {"start": 2454.14, "end": 2455.4, "word": " واحد", "probability": 0.978271484375}, {"start": 2455.4, "end": 2456.14, "word": " زائد", "probability": 0.9773763020833334}, {"start": 2456.14, "end": 2456.66, "word": " X", "probability": 0.994140625}], "temperature": 1.0}, {"id": 100, "seek": 249523, "start": 2489.46, "end": 2495.24, "text": "هاتلي دالة تمثل هذه الـ Power Series", "tokens": [3224, 9307, 20292, 11778, 6027, 3660, 6055, 2304, 12984, 1211, 29538, 2423, 39184, 7086, 13934], "avg_logprob": -0.5830078013241291, "compression_ratio": 0.8870967741935484, "no_speech_prob": 0.0, "words": [{"start": 2489.46, "end": 2490.86, "word": "هاتلي", "probability": 0.4803466796875}, {"start": 2490.86, "end": 2491.6, "word": " دالة", "probability": 0.8470052083333334}, {"start": 2491.6, "end": 2493.3, "word": " تمثل", "probability": 0.75128173828125}, {"start": 2493.3, "end": 2493.74, "word": " هذه", "probability": 0.6875}, {"start": 2493.74, "end": 2493.92, "word": " الـ", "probability": 0.30218505859375}, {"start": 2493.92, "end": 2494.42, "word": " Power", "probability": 0.323486328125}, {"start": 2494.42, "end": 2495.24, "word": " Series", "probability": 0.90673828125}], "temperature": 1.0}, {"id": 101, "seek": 252926, "start": 2502.56, "end": 2529.26, "text": "بعد هيك النتيجة اللى تحصل عليها بدك تستخدمها في الحصول على power series لتو functions اللى عندك يعني عملية عكسية ماتيني power series بد اتدلتها تبعتها يبقى سعر اندي دالة و سعر power series بد تستخدم هذه النتيجة للحصول على شكل ال power series لها تين اتدلتين", "tokens": [3555, 22488, 39896, 4117, 28239, 31371, 7435, 3660, 13672, 7578, 6055, 5016, 36520, 25894, 11296, 47525, 4117, 6055, 14851, 9778, 40448, 11296, 8978, 21542, 9381, 12610, 15844, 1347, 2638, 5296, 2655, 2407, 6828, 13672, 7578, 43242, 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واحد ناقص الأساس هذا شو بيعطينا؟ هذا بيعطينا أن ال S يساوي واحد على واحد زائد ال X أليس هذه function في X؟", "tokens": [2670, 264, 2638, 318, 2423, 318, 6055, 3794, 995, 45865, 21542, 3215, 16247, 12610, 15844, 36764, 24401, 8717, 995, 4587, 9381, 16247, 3794, 32277, 23758, 13412, 2407, 4724, 1829, 3615, 9566, 1829, 8315, 22807, 23758, 4724, 1829, 3615, 9566, 1829, 8315, 14739, 2423, 318, 7251, 3794, 995, 45865, 36764, 24401, 15844, 36764, 24401, 30767, 16373, 3215, 2423, 1783, 5551, 20292, 3794, 29538, 2445, 8978, 1783, 22807], "avg_logprob": -0.1921641719875051, "compression_ratio": 1.5894039735099337, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2669.44, "end": 2670.18, "word": "of", "probability": 0.50048828125}, {"start": 2670.18, "end": 2671.4, "word": " the", "probability": 0.86865234375}, {"start": 2671.4, "end": 2672.52, "word": " series", "probability": 0.92724609375}, {"start": 2672.52, "end": 2673.8, "word": " S", "probability": 0.68359375}, {"start": 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