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+{"segments": [{"id": 1, "seek": 3452, "start": 5.28, "end": 34.52, "text": "بسم الله الرحمن الرحيم المحاضرة الرابعة مساق تحليل حقيقة 2 لطلبة الجامعة الإسلامية كلية العلوم قسم الرياضيات نستكمل الحديث عن نظرية القيمة المتوسطة أو the mean value theorem وما يتعلق بذلك تحدثنا المرة الماضية", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 5016, 46958, 25720, 34892, 16758, 27884, 47524, 995, 4587, 6055, 5016, 20292, 1211, 11331, 38436, 28671, 568, 5296, 9566, 46152, 3660, 25724, 10943, 27884, 33688, 3794, 37440, 10632, 28242, 10632, 18863, 1211, 20498, 12174, 38251, 2423, 16572, 46958, 1829, 9307, 8717, 14851, 24793, 1211, 21542, 16254, 12984, 18871, 8717, 19913, 2288, 10632, 25062, 32640, 3660, 9673, 2655, 41779, 9566, 3660, 34051, 264, 914, 2158, 20904, 4032, 15042, 7251, 2655, 30241, 4587, 4724, 8848, 23275, 6055, 24401, 12984, 8315, 9673, 25720, 9673, 46958, 10632], "avg_logprob": -0.08701795022538368, "compression_ratio": 1.7632850241545894, "no_speech_prob": 2.682209014892578e-06, "words": [{"start": 5.28, "end": 5.64, "word": "بسم", "probability": 0.887939453125}, {"start": 5.64, "end": 5.86, "word": " الله", "probability": 0.953125}, {"start": 5.86, "end": 6.26, "word": " الرحمن", "probability": 0.9762369791666666}, {"start": 6.26, "end": 6.82, "word": " الرحيم", "probability": 0.9949544270833334}, {"start": 6.82, "end": 8.6, "word": " المحاضرة", "probability": 0.970703125}, {"start": 8.6, "end": 9.52, "word": " الرابعة", "probability": 0.9716796875}, {"start": 9.52, "end": 10.82, "word": " مساق", "probability": 0.92041015625}, {"start": 10.82, "end": 12.08, "word": " تحليل", "probability": 0.9718017578125}, {"start": 12.08, "end": 12.64, "word": " حقيقة", "probability": 0.7757975260416666}, {"start": 12.64, "end": 13.06, "word": " 2", "probability": 0.70947265625}, {"start": 13.06, "end": 15.2, "word": " لطلبة", "probability": 0.950439453125}, {"start": 15.2, "end": 15.64, "word": " الجامعة", "probability": 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minimum معرفناها المرة الماضية و أتحدثنا أيضًا عن اللي هو ال interior extreme theorem ال interior extreme theorem اللي هي جوابتنا على السؤال اللي بنحكي فيه", "tokens": [2304, 3615, 1863, 7578, 4972, 1279, 265, 1696, 8608, 2407, 16606, 4972, 6674, 34051, 4972, 7285, 34051, 4724, 2304, 3615, 1863, 7578, 5551, 34740, 2423, 8236, 2423, 2654, 6674, 4032, 2423, 2654, 7285, 20449, 28480, 8315, 11296, 9673, 25720, 9673, 46958, 10632, 4032, 5551, 2655, 24401, 12984, 8315, 36632, 11242, 14111, 995, 18871, 13672, 1829, 31439, 2423, 10636, 8084, 20904, 2423, 10636, 8084, 20904, 13672, 1829, 39896, 10874, 14407, 3555, 2655, 8315, 15844, 21136, 33604, 6027, 13672, 1829, 44945, 5016, 4117, 1829, 8978, 3224], "avg_logprob": -0.20790441386839922, "compression_ratio": 1.8349514563106797, "no_speech_prob": 1.430511474609375e-06, "words": [{"start": 35.99000000000001, "end": 36.95, "word": "معنى", "probability": 0.85107421875}, {"start": 36.95, "end": 37.35, "word": " relative", "probability": 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44.47, "word": " ال", "probability": 0.299072265625}, {"start": 44.47, "end": 45.05, "word": " local", "probability": 0.57373046875}, {"start": 45.05, "end": 45.75, "word": " maximum", "probability": 0.96875}, {"start": 45.75, "end": 46.47, "word": " و", "probability": 0.54248046875}, {"start": 46.47, "end": 46.79, "word": " ال", "probability": 0.93212890625}, {"start": 46.79, "end": 47.15, "word": " local", "probability": 0.85546875}, {"start": 47.15, "end": 47.45, "word": " minimum", "probability": 0.97705078125}, {"start": 47.45, "end": 48.21, "word": " معرفناها", "probability": 0.8594970703125}, {"start": 48.21, "end": 48.53, "word": " المرة", "probability": 0.96484375}, {"start": 48.53, "end": 49.09, "word": " الماضية", "probability": 0.9928385416666666}, {"start": 49.09, "end": 51.17, "word": " و", "probability": 0.28369140625}, {"start": 51.17, "end": 52.09, "word": " أتحدثنا", "probability": 0.865234375}, {"start": 52.09, "end": 52.69, "word": " أيضًا", "probability": 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هي", "probability": 0.93115234375}, {"start": 60.29, "end": 61.49, "word": " جوابتنا", "probability": 0.926953125}, {"start": 61.49, "end": 61.75, "word": " على", "probability": 0.91455078125}, {"start": 61.75, "end": 62.33, "word": " السؤال", "probability": 0.9962565104166666}, {"start": 62.33, "end": 62.49, "word": " اللي", "probability": 0.969970703125}, {"start": 62.49, "end": 63.03, "word": " بنحكي", "probability": 0.9583740234375}, {"start": 63.03, "end": 63.43, "word": " فيه", "probability": 0.966552734375}], "temperature": 1.0}, {"id": 3, "seek": 8523, "start": 63.77, "end": 85.23, "text": "أين يمكن إيجاد القيم العظمى أو القيم الصغرى النظرية اللي بتحكي كانت ان لو كانت C عبارة عن interior point اللي هي ال interval I اللي عندها اللي هي ال function F ال derivative موجودة", "tokens": [10721, 9957, 7251, 43020, 11933, 1829, 7435, 18513, 25062, 32640, 18863, 19913, 2304, 7578, 34051, 25062, 32640, 31767, 17082, 2288, 7578, 28239, 19913, 2288, 10632, 13672, 1829, 39894, 5016, 4117, 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{"start": 69.17, "end": 70.75, "word": " النظرية", "probability": 0.81280517578125}, {"start": 70.75, "end": 71.09, "word": " اللي", "probability": 0.662353515625}, {"start": 71.09, "end": 72.01, "word": " بتحكي", "probability": 0.911376953125}, {"start": 72.01, "end": 72.37, "word": " كانت", "probability": 0.8203125}, {"start": 72.37, "end": 72.55, "word": " ان", "probability": 0.380126953125}, {"start": 72.55, "end": 72.81, "word": " لو", "probability": 0.91162109375}, {"start": 72.81, "end": 73.29, "word": " كانت", "probability": 0.958251953125}, {"start": 73.29, "end": 73.61, "word": " C", "probability": 0.52685546875}, {"start": 73.61, "end": 74.53, "word": " عبارة", "probability": 0.9833984375}, {"start": 74.53, "end": 74.73, "word": " عن", "probability": 0.9912109375}, {"start": 74.73, "end": 75.35, "word": " interior", "probability": 0.6748046875}, {"start": 75.35, "end": 76.29, "word": " point", "probability": 0.98388671875}, {"start": 76.29, "end": 77.55, "word": " اللي", 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84.35, "word": " derivative", "probability": 0.9091796875}, {"start": 84.35, "end": 85.23, "word": " موجودة", "probability": 0.9832763671875}], "temperature": 1.0}, {"id": 4, "seek": 11248, "start": 85.88, "end": 112.48, "text": "بقول لو كان عند النقطة هذه في relative extremum سواء minimum أو maximum لل F عنده نقطة C قطعا ال F prime of C هتساوي 0 ومن هنا استقينا أن أين يمكن إيجاد النقطة العظمى والنقطة الصغيرة المحلية وقلنا هي في أحد ثلاث مناطق اللي هو أما F prime بتساوي 0", "tokens": [3555, 39648, 45164, 25961, 43242, 28239, 47432, 3660, 29538, 8978, 4972, 4040, 449, 8608, 2407, 16606, 7285, 34051, 6674, 24976, 479, 43242, 3224, 8717, 47432, 3660, 383, 12174, 9566, 3615, 995, 2423, 479, 5835, 295, 383, 8032, 2655, 3794, 995, 45865, 1958, 4032, 27842, 34105, 44713, 38436, 8315, 14739, 5551, 9957, 7251, 43020, 11933, 1829, 7435, 18513, 28239, 47432, 3660, 18863, 19913, 2304, 7578, 16070, 1863, 47432, 3660, 31767, 17082, 48923, 9673, 5016, 1211, 10632, 4032, 4587, 1211, 8315, 39896, 8978, 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سواء", "probability": 0.8933919270833334}, {"start": 92.14, "end": 92.58, "word": " minimum", "probability": 0.8935546875}, {"start": 92.58, "end": 93.14, "word": " أو", "probability": 0.71435546875}, {"start": 93.14, "end": 93.86, "word": " maximum", "probability": 0.97509765625}, {"start": 93.86, "end": 94.26, "word": " لل", "probability": 0.85791015625}, {"start": 94.26, "end": 94.6, "word": " F", "probability": 0.46630859375}, {"start": 94.6, "end": 95.02, "word": " عنده", "probability": 0.943603515625}, {"start": 95.02, "end": 95.34, "word": " نقطة", "probability": 0.9488932291666666}, {"start": 95.34, "end": 95.6, "word": " C", "probability": 0.7138671875}, {"start": 95.6, "end": 96.46, "word": " قطعا", "probability": 0.9256591796875}, {"start": 96.46, "end": 96.56, "word": " ال", "probability": 0.83984375}, {"start": 96.56, "end": 96.74, "word": " F", "probability": 0.6708984375}, {"start": 96.74, "end": 97.08, "word": " prime", "probability": 0.44482421875}, {"start": 97.08, 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"probability": 0.885009765625}, {"start": 105.04, "end": 106.12, "word": " والنقطة", "probability": 0.7559814453125}, {"start": 106.12, "end": 106.56, "word": " الصغيرة", "probability": 0.841796875}, {"start": 106.56, "end": 107.32, "word": " المحلية", "probability": 0.981689453125}, {"start": 107.32, "end": 108.06, "word": " وقلنا", "probability": 0.7933349609375}, {"start": 108.06, "end": 108.22, "word": " هي", "probability": 0.6806640625}, {"start": 108.22, "end": 108.4, "word": " في", "probability": 0.93994140625}, {"start": 108.4, "end": 108.6, "word": " أحد", "probability": 0.95166015625}, {"start": 108.6, "end": 108.94, "word": " ثلاث", "probability": 0.8907470703125}, {"start": 108.94, "end": 109.56, "word": " مناطق", "probability": 0.96044921875}, {"start": 109.56, "end": 110.06, "word": " اللي", "probability": 0.85009765625}, {"start": 110.06, "end": 110.3, "word": " هو", "probability": 0.8154296875}, {"start": 110.3, "end": 110.66, "word": " أما", "probability": 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{"start": 148.4, "end": 148.7, "word": " و", "probability": 0.9755859375}, {"start": 148.7, "end": 149.06, "word": " كانت", "probability": 0.8828125}, {"start": 149.06, "end": 149.26, "word": " هذه", "probability": 0.5478515625}, {"start": 149.26, "end": 149.4, "word": " ال", "probability": 0.970703125}, {"start": 149.4, "end": 149.88, "word": " function", "probability": 0.80029296875}, {"start": 149.88, "end": 150.74, "word": " is", "probability": 0.6689453125}, {"start": 150.74, "end": 151.44, "word": " continuous", "probability": 0.9072265625}, {"start": 151.44, "end": 151.88, "word": " على", "probability": 0.5224609375}, {"start": 151.88, "end": 152.58, "word": " closed", "probability": 0.6484375}, {"start": 152.58, "end": 153.98, "word": " interval", "probability": 0.97900390625}], "temperature": 1.0}, {"id": 7, "seek": 17257, "start": 155.05, "end": 172.57, "text": "اللي هي من a لعند b و differentiable على ال open interval من a لb و أيضا وضعنا شرط أن f of a بيساوي f of b بيساوي سفر بقولنا ال f differentiable on a و b", "tokens": [6027, 20292, 39896, 9154, 257, 5296, 3615, 41260, 272, 4032, 819, 9364, 15844, 2423, 1269, 15035, 9154, 257, 5296, 65, 4032, 36632, 11242, 995, 4032, 11242, 3615, 8315, 13412, 2288, 9566, 14739, 283, 295, 257, 4724, 1829, 3794, 995, 45865, 283, 295, 272, 4724, 1829, 3794, 995, 45865, 8608, 5172, 2288, 4724, 39648, 8315, 2423, 283, 819, 9364, 322, 257, 4032, 272], "avg_logprob": -0.25173611300332205, "compression_ratio": 1.4689655172413794, "no_speech_prob": 4.1365623474121094e-05, "words": [{"start": 155.05, "end": 155.39, "word": "اللي", "probability": 0.768798828125}, {"start": 155.39, "end": 155.71, "word": " هي", "probability": 0.72802734375}, {"start": 155.71, "end": 156.01, "word": " من", "probability": 0.9853515625}, {"start": 156.01, "end": 156.23, "word": " a", "probability": 0.287353515625}, {"start": 156.23, "end": 156.63, "word": " لعند", "probability": 0.8380533854166666}, {"start": 156.63, "end": 156.97, "word": " b", 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"word": " بمعنى", "probability": 0.97646484375}, {"start": 193.03, "end": 193.55, "word": " آخر", "probability": 0.83935546875}, {"start": 193.55, "end": 194.45, "word": " يوجد", "probability": 0.9671223958333334}, {"start": 194.45, "end": 194.97, "word": " مماس", "probability": 0.9755859375}, {"start": 194.97, "end": 196.07, "word": " عند", "probability": 0.541015625}, {"start": 196.07, "end": 196.37, "word": " هذه", "probability": 0.634765625}, {"start": 196.37, "end": 196.97, "word": " النقطة", "probability": 0.9925130208333334}, {"start": 196.97, "end": 197.51, "word": " يوازي", "probability": 0.89453125}, {"start": 197.51, "end": 198.03, "word": " محور", "probability": 0.9864908854166666}, {"start": 198.03, "end": 198.77, "word": " الـ", "probability": 0.7451171875}, {"start": 198.77, "end": 199.21, "word": " CNET", "probability": 0.47491455078125}], "temperature": 1.0}, {"id": 9, "seek": 22347, "start": 199.61, "end": 223.47, "text": "بعد ذلك طبعا تحدثنا عن الـ Mean Value Theorem الـ Mean Value Theorem اللي كانت أيضا على الرسم خلينا نشوف الـ Mean Value Theorem قالت إن لو كانت الـ function is continuous على closed interval من A لB وكانت اللي هي differentiable على الـ open interval A وB", "tokens": [3555, 22488, 29910, 23275, 23032, 3555, 3615, 995, 6055, 24401, 12984, 8315, 18871, 2423, 39184, 12302, 39352, 440, 37956, 2423, 39184, 12302, 39352, 440, 37956, 13672, 1829, 25961, 2655, 36632, 11242, 995, 15844, 34892, 38251, 16490, 1211, 9957, 995, 8717, 8592, 38688, 2423, 39184, 12302, 39352, 440, 37956, 50239, 2655, 36145, 45164, 25961, 2655, 2423, 39184, 2445, 307, 10957, 15844, 5395, 15035, 9154, 316, 5296, 33, 4032, 41361, 2655, 13672, 1829, 39896, 819, 9364, 15844, 2423, 39184, 1269, 15035, 316, 4032, 33], "avg_logprob": -0.2217620428068092, "compression_ratio": 1.6778846153846154, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 199.61, "end": 200.01, "word": "بعد", "probability": 0.87255859375}, {"start": 200.01, "end": 200.39, "word": " ذلك", 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اللي هي معلومات معهودة من ال calculus اللي هي أنه لو كان في عندنا دالتين F و G و هذولة الدالتين اللي عندنا اللي هن .. اللي هن نفس المشتقة على الفترة A و B Open", "tokens": [10721, 1829, 11242, 14111, 995, 3925, 1833, 822, 46740, 24192, 28239, 19913, 2288, 10632, 4724, 43042, 3224, 13672, 1829, 39896, 20449, 1211, 20498, 9307, 20449, 3224, 23328, 3660, 9154, 2423, 33400, 13672, 1829, 39896, 14739, 3224, 45164, 25961, 8978, 43242, 8315, 11778, 6027, 2655, 9957, 479, 4032, 460, 4032, 8032, 8848, 12610, 3660, 32748, 6027, 2655, 9957, 13672, 1829, 43242, 8315, 13672, 1829, 8032, 1863, 4386, 13672, 1829, 8032, 1863, 8717, 36178, 9673, 8592, 2655, 28671, 15844, 27188, 2655, 25720, 316, 4032, 363, 7238], "avg_logprob": -0.19522059454637417, "compression_ratio": 1.6528497409326426, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 314.58, "end": 315.34, "word": "أيضًا", "probability": 0.707177734375}, {"start": 315.34, "end": 316.02, "word": " Corollary", "probability": 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ال", "probability": 0.99072265625}, {"start": 352.88, "end": 353.46, "word": " interval", "probability": 0.360595703125}, {"start": 353.46, "end": 354.68, "word": " قلنا", "probability": 0.7998046875}, {"start": 354.68, "end": 354.96, "word": " أن", "probability": 0.50244140625}, {"start": 354.96, "end": 355.4, "word": " F", "probability": 0.640625}, {"start": 355.4, "end": 355.78, "word": " is", "probability": 0.958984375}, {"start": 355.78, "end": 356.72, "word": " increasing", "probability": 0.9736328125}, {"start": 356.72, "end": 358.2, "word": " إذا", "probability": 0.935791015625}, {"start": 358.2, "end": 358.74, "word": " كانت", "probability": 0.98486328125}, {"start": 358.74, "end": 358.9, "word": " اللى", "probability": 0.91162109375}, {"start": 358.9, "end": 359.26, "word": " هى", "probability": 0.914794921875}], "temperature": 1.0}, {"id": 16, "seek": 37603, "start": 360.25, "end": 376.03, "text": "أخدنا أي نقطتين في الـ I X1 و X2 بحقق ان X1 أصغر من X2 إذا قدلنا هذا أن أف X1 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{"id": 18, "seek": 42155, "start": 392.75, "end": 421.55, "text": "في المقابل أيضًا في تعريف حاجة اسمها برضه ذكرناه هو strictly increasing أو strictly decreasing strictly increasing أو strictly decreasing نحكي عن ال strictly increasing بتكون اللي هي تحقق مالي لو x1 و x2 في ال I و x1 أصغر من x2 هذا بيقديلي إلى f of x1 strictly أصغر من f of x2 مع عدم إمكانية المساوية", "tokens": [41185, 9673, 4587, 16758, 1211, 36632, 11242, 14111, 995, 8978, 37279, 16572, 5172, 11331, 26108, 3660, 24525, 2304, 11296, 4724, 43042, 3224, 29910, 37983, 8315, 3224, 31439, 20792, 5662, 34051, 20792, 23223, 20792, 5662, 34051, 20792, 23223, 8717, 5016, 4117, 1829, 18871, 2423, 20792, 5662, 39894, 30544, 13672, 1829, 39896, 6055, 5016, 4587, 4587, 3714, 6027, 1829, 45164, 2031, 16, 4032, 2031, 17, 8978, 2423, 286, 4032, 2031, 16, 5551, 9381, 17082, 2288, 9154, 2031, 17, 23758, 4724, 1829, 4587, 16254, 20292, 30731, 283, 295, 2031, 16, 20792, 5551, 9381, 17082, 2288, 9154, 283, 295, 2031, 17, 20449, 6225, 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449.7, "text": "الان similarly for الـ F is اللي هو strictly decreasing هذا اتحدثنا فيه المرة الماضية النظرية اللي هي let F من I لعند R be differentiable اللي هي أوصلنا عند هذه النظرية خلينا نشوف هذه النظرية و نتفحص إيش هي نظرية بتقول و من ثم نشوف لماذا", "tokens": [6027, 7649, 14138, 337, 2423, 39184, 479, 307, 13672, 1829, 31439, 20792, 23223, 23758, 1975, 2655, 24401, 12984, 8315, 8978, 3224, 9673, 25720, 9673, 46958, 10632, 28239, 19913, 2288, 10632, 13672, 1829, 39896, 718, 479, 9154, 286, 5296, 3615, 41260, 497, 312, 819, 9364, 13672, 1829, 39896, 34051, 36520, 8315, 43242, 29538, 28239, 19913, 2288, 10632, 16490, 1211, 9957, 995, 8717, 8592, 38688, 29538, 28239, 19913, 2288, 10632, 4032, 8717, 2655, 5172, 5016, 9381, 11933, 1829, 8592, 39896, 8717, 19913, 2288, 10632, 39894, 39648, 4032, 9154, 38637, 2304, 8717, 8592, 38688, 32767, 45636, 995], "avg_logprob": -0.1837171008712367, "compression_ratio": 1.7031963470319635, "no_speech_prob": 2.384185791015625e-07, "words": 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let F من I لعنب R be differentiable on", "tokens": [6027, 20292, 31439, 39896, 20328, 5016, 1829, 5016, 3660, 18871, 16254, 8717, 19913, 2288, 10632, 39894, 39648, 20292, 20904, 1386, 13, 17, 13, 22, 13672, 1829, 39894, 5016, 4117, 1829, 28239, 19913, 2288, 10632, 39894, 39648, 20292, 45164, 25961, 18871, 16254, 479, 718, 479, 9154, 286, 5296, 3615, 1863, 3555, 497, 312, 819, 9364, 322], "avg_logprob": -0.199358251744083, "compression_ratio": 1.4, "no_speech_prob": 4.303455352783203e-05, "words": [{"start": 450.1, "end": 450.48, "word": "اللي", "probability": 0.799072265625}, {"start": 450.48, "end": 450.9, "word": " هو", "probability": 0.69189453125}, {"start": 450.9, "end": 451.64, "word": " هي", "probability": 0.70361328125}, {"start": 451.64, "end": 453.1, "word": " صحيحة", "probability": 0.98828125}, {"start": 453.1, "end": 458.96, "word": " عندي", "probability": 0.70556640625}, {"start": 458.96, "end": 459.76, "word": " نظرية", "probability": 0.918212890625}, {"start": 459.76, 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538.95, "end": 565.13, "text": "و هنبرهن اللي هو A أو B في الكتاب نبرهن A خلّينا نبرهن مين نبرهن B و هتكون A similarly for B الان بي .. بدنا نفترض suppose that F is decreasing on I", "tokens": [2407, 8032, 1863, 26890, 3224, 1863, 13672, 1829, 31439, 316, 34051, 363, 8978, 33251, 2655, 16758, 8717, 26890, 3224, 1863, 316, 16490, 1211, 11703, 9957, 995, 8717, 26890, 3224, 1863, 3714, 9957, 8717, 26890, 3224, 1863, 363, 4032, 8032, 2655, 30544, 316, 14138, 337, 363, 2423, 7649, 4724, 1829, 4386, 47525, 8315, 8717, 5172, 2655, 43042, 7297, 300, 479, 307, 23223, 322, 286], "avg_logprob": -0.21594238048419356, "compression_ratio": 1.3584905660377358, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 538.95, "end": 539.31, "word": "و", "probability": 0.86181640625}, {"start": 539.31, "end": 540.19, "word": " هنبرهن", "probability": 0.84189453125}, {"start": 540.19, "end": 540.77, "word": " اللي", "probability": 0.8837890625}, {"start": 540.77, "end": 541.27, "word": " هو", 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بدنا الأن نيجي ل conversely بدنا نفترض هذا أصحى و أصحى و صفر و نوصل لمين لل F is decreasing نيجي الأن conversely و نشوف كيف نبرهن conversely الأن conversely", "tokens": [3224, 15730, 13672, 1829, 31439, 25724, 11622, 38207, 16247, 12610, 9154, 28239, 19913, 2288, 10632, 9154, 13672, 1829, 31439, 363, 14739, 3224, 47525, 8315, 16247, 1863, 8717, 1829, 7435, 1829, 5296, 2615, 736, 47525, 8315, 8717, 5172, 2655, 43042, 23758, 5551, 9381, 5016, 7578, 4032, 5551, 9381, 5016, 7578, 4032, 20328, 5172, 2288, 4032, 8717, 2407, 36520, 5296, 2304, 9957, 24976, 479, 307, 23223, 8717, 1829, 7435, 1829, 16247, 1863, 2615, 736, 4032, 8717, 8592, 38688, 9122, 33911, 8717, 26890, 3224, 1863, 2615, 736, 16247, 1863, 2615, 736], "avg_logprob": -0.24947332532218333, "compression_ratio": 1.7351351351351352, "no_speech_prob": 1.4901161193847656e-05, "words": [{"start": 833.32, "end": 834.5, "word": "هذا", "probability": 0.79345703125}, {"start": 834.5, "end": 834.6, "word": " اللي", "probability": 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"probability": 0.99267578125}, {"start": 911.45, "end": 911.59, "word": " ما", "probability": 0.595703125}, {"start": 911.59, "end": 911.73, "word": " هي", "probability": 0.6845703125}, {"start": 911.73, "end": 912.59, "word": " automatic", "probability": 0.82470703125}, {"start": 912.59, "end": 912.85, "word": " F", "probability": 0.453369140625}, {"start": 912.85, "end": 913.03, "word": " of", "probability": 0.642578125}, {"start": 913.03, "end": 913.41, "word": " x1", "probability": 0.96240234375}, {"start": 913.41, "end": 913.75, "word": " بيساوي", "probability": 0.87041015625}, {"start": 913.75, "end": 913.93, "word": " F", "probability": 0.9765625}, {"start": 913.93, "end": 914.07, "word": " of", "probability": 0.96875}, {"start": 914.07, "end": 914.49, "word": " x2", "probability": 0.993896484375}, {"start": 914.49, "end": 914.71, "word": " يعني", "probability": 0.930419921875}, {"start": 914.71, "end": 915.53, "word": " متحققة", "probability": 0.9498291015625}], "temperature": 1.0}, {"id": 39, "seek": 94162, "start": 915.9, "end": 941.62, "text": "إذن الان x1 أصغر من x2 عملتها strictly عشان بتعمل منها interval وحالتي ال x1 بيساوي x2 is a trivial case تتحقق مدامة x1 أصغر تساوي x2 إذن عشان a function f of x1 بيساوي f of x2 إذا التحقق اللي هي مين ال decreasing واضحة الان x1 أصغر من x2 الآن we apply", "tokens": [28814, 8848, 1863, 2423, 7649, 2031, 16, 5551, 9381, 17082, 2288, 9154, 2031, 17, 6225, 42213, 2655, 11296, 20792, 6225, 8592, 7649, 39894, 25957, 1211, 9154, 11296, 15035, 4032, 5016, 6027, 31371, 2423, 2031, 16, 4724, 1829, 3794, 995, 45865, 2031, 17, 307, 257, 26703, 1389, 6055, 2655, 5016, 4587, 4587, 3714, 3215, 10943, 3660, 2031, 16, 5551, 9381, 17082, 2288, 6055, 3794, 995, 45865, 2031, 17, 11933, 8848, 1863, 6225, 8592, 7649, 257, 2445, 283, 295, 2031, 16, 4724, 1829, 3794, 995, 45865, 283, 295, 2031, 17, 11933, 15730, 16712, 5016, 4587, 4587, 13672, 1829, 39896, 3714, 9957, 2423, 23223, 4032, 46958, 5016, 3660, 2423, 7649, 2031, 16, 5551, 9381, 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0.93154296875}, {"start": 929.62, "end": 929.76, "word": " f", "probability": 0.91064453125}, {"start": 929.76, "end": 929.88, "word": " of", "probability": 0.9345703125}, {"start": 929.88, "end": 931.02, "word": " x2", "probability": 0.9892578125}, {"start": 931.02, "end": 931.26, "word": " إذا", "probability": 0.813720703125}, {"start": 931.26, "end": 932.1, "word": " التحقق", "probability": 0.8665771484375}, {"start": 932.1, "end": 932.58, "word": " اللي", "probability": 0.88818359375}, {"start": 932.58, "end": 932.8, "word": " هي", "probability": 0.7119140625}, {"start": 932.8, "end": 933.16, "word": " مين", "probability": 0.508636474609375}, {"start": 933.16, "end": 933.4, "word": " ال", "probability": 0.748046875}, {"start": 933.4, "end": 933.88, "word": " decreasing", "probability": 0.78466796875}, {"start": 933.88, "end": 935.78, "word": " واضحة", "probability": 0.79302978515625}, {"start": 935.78, "end": 937.2, "word": " الان", "probability": 0.517242431640625}, {"start": 937.2, "end": 938.44, "word": " x1", "probability": 0.899658203125}, {"start": 938.44, "end": 938.68, "word": " أصغر", "probability": 0.9891357421875}, {"start": 938.68, "end": 938.78, "word": " من", "probability": 0.99462890625}, {"start": 938.78, "end": 939.34, "word": " x2", "probability": 0.99658203125}, {"start": 939.34, "end": 940.34, "word": " الآن", "probability": 0.6263427734375}, {"start": 940.34, "end": 941.1, "word": " we", "probability": 0.88427734375}, {"start": 941.1, "end": 941.62, "word": " apply", "probability": 0.9560546875}], "temperature": 1.0}, {"id": 40, "seek": 96420, "start": 945.1, "end": 964.2, "text": "الـ Mean Value Theorem لأن احنا هذه نبارع كورولرز أو نظريات على الـ Mean Value Theorem فالمتوقع أن نستخدم الـ Mean Value Theorem في أثباتها فهنا سنستخدم الـ Mean Value Theorem نطبق الـ Mean Value Theorem على الانترفل الموجود بين X1 و X2", "tokens": [6027, 39184, 12302, 39352, 440, 37956, 5296, 33456, 1975, 5016, 8315, 29538, 8717, 3555, 9640, 3615, 9122, 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"probability": 0.736083984375}, {"start": 946.96, "end": 947.5, "word": " احنا", "probability": 0.748291015625}, {"start": 947.5, "end": 947.76, "word": " هذه", "probability": 0.1513671875}, {"start": 947.76, "end": 948.16, "word": " نبارع", "probability": 0.440673828125}, {"start": 948.16, "end": 948.88, "word": " كورولرز", "probability": 0.550634765625}, {"start": 948.88, "end": 949.04, "word": " أو", "probability": 0.76953125}, {"start": 949.04, "end": 949.72, "word": " نظريات", "probability": 0.982177734375}, {"start": 949.72, "end": 950.32, "word": " على", "probability": 0.79150390625}, {"start": 950.32, "end": 950.5, "word": " الـ", "probability": 0.83251953125}, {"start": 950.5, "end": 950.64, "word": " Mean", "probability": 0.8076171875}, {"start": 950.64, "end": 950.94, "word": " Value", "probability": 0.984375}, {"start": 950.94, "end": 951.24, "word": " Theorem", "probability": 0.916015625}, {"start": 951.24, "end": 952.18, "word": " فالمتوقع", "probability": 0.85966796875}, {"start": 952.18, "end": 952.38, "word": " أن", "probability": 0.44189453125}, {"start": 952.38, "end": 952.96, "word": " نستخدم", "probability": 0.962646484375}, {"start": 952.96, "end": 953.12, "word": " الـ", "probability": 0.863525390625}, {"start": 953.12, "end": 953.24, "word": " Mean", "probability": 0.9013671875}, {"start": 953.24, "end": 953.54, "word": " Value", "probability": 0.986328125}, {"start": 953.54, "end": 953.76, "word": " Theorem", "probability": 0.91455078125}, {"start": 953.76, "end": 953.88, "word": " في", "probability": 0.466796875}, {"start": 953.88, "end": 954.48, "word": " أثباتها", "probability": 0.8984375}, {"start": 954.48, "end": 955.24, "word": " فهنا", "probability": 0.8792317708333334}, {"start": 955.24, "end": 955.98, "word": " سنستخدم", "probability": 0.89033203125}, {"start": 955.98, "end": 956.18, "word": " الـ", "probability": 0.84375}, {"start": 956.18, "end": 956.44, "word": " Mean", "probability": 0.85498046875}, {"start": 956.44, "end": 956.84, "word": " Value", "probability": 0.9853515625}, {"start": 956.84, "end": 957.28, "word": " Theorem", "probability": 0.92333984375}, {"start": 957.28, "end": 958.34, "word": " نطبق", "probability": 0.6715087890625}, {"start": 958.34, "end": 958.34, "word": " الـ", "probability": 0.505523681640625}, {"start": 958.34, "end": 958.66, "word": " Mean", "probability": 0.91748046875}, {"start": 958.66, "end": 959.0, "word": " Value", "probability": 0.98876953125}, {"start": 959.0, "end": 959.64, "word": " Theorem", "probability": 0.910400390625}, {"start": 959.64, "end": 960.4, "word": " على", "probability": 0.6494140625}, {"start": 960.4, "end": 961.28, "word": " الانترفل", "probability": 0.56768798828125}, {"start": 961.28, "end": 961.5, "word": " الموجود", "probability": 0.441162109375}, {"start": 961.5, "end": 961.68, "word": " بين", "probability": 0.57861328125}, {"start": 961.68, "end": 962.88, "word": " X1", "probability": 0.511962890625}, {"start": 962.88, "end": 963.6, "word": " و", "probability": 0.90283203125}, {"start": 963.6, "end": 964.2, "word": " X2", "probability": 0.8427734375}], "temperature": 1.0}, {"id": 41, "seek": 97729, "start": 964.71, "end": 977.29, "text": "طبعاً عندي F هذه X1 و X2 عبارة عن جزئية من مين؟ من الـ I إذا الـ F is differentiable عليها مادام differentiable إذا continuous علي close و differentiable علي open لإنها differentiable علي كلها", "tokens": [9566, 3555, 3615, 995, 14111, 18871, 16254, 479, 29538, 1783, 16, 4032, 1783, 17, 6225, 3555, 9640, 3660, 18871, 10874, 11622, 19986, 10632, 9154, 3714, 9957, 22807, 9154, 2423, 39184, 286, 11933, 15730, 2423, 39184, 479, 307, 819, 9364, 25894, 11296, 3714, 18513, 10943, 819, 9364, 11933, 15730, 10957, 25894, 1998, 4032, 819, 9364, 25894, 1269, 5296, 28814, 1863, 11296, 819, 9364, 25894, 28242, 11296], "avg_logprob": -0.30539771824172046, "compression_ratio": 1.5647058823529412, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 964.71, "end": 965.15, "word": "طبعاً", "probability": 0.796044921875}, {"start": 965.15, "end": 965.47, "word": " عندي", "probability": 0.5469970703125}, {"start": 965.47, "end": 965.83, "word": " F", "probability": 0.64013671875}, {"start": 965.83, "end": 966.75, "word": " هذه", "probability": 0.232177734375}, {"start": 966.75, "end": 967.15, "word": " X1", "probability": 0.8583984375}, {"start": 967.15, "end": 967.27, "word": " و", "probability": 0.94580078125}, {"start": 967.27, "end": 967.69, "word": " X2", "probability": 0.888671875}, {"start": 967.69, "end": 968.19, "word": " عبارة", "probability": 0.99560546875}, {"start": 968.19, "end": 968.39, "word": " عن", "probability": 0.990234375}, {"start": 968.39, "end": 968.81, "word": " جزئية", "probability": 0.9376220703125}, {"start": 968.81, "end": 968.99, "word": " من", "probability": 0.99072265625}, {"start": 968.99, "end": 969.27, "word": " مين؟", "probability": 0.634765625}, {"start": 969.27, "end": 969.39, "word": " من", "probability": 0.9638671875}, {"start": 969.39, "end": 969.65, "word": " الـ", "probability": 0.863525390625}, {"start": 969.65, "end": 969.81, "word": " I", "probability": 0.62353515625}, {"start": 969.81, "end": 970.33, "word": " إذا", "probability": 0.6507568359375}, {"start": 970.33, "end": 970.55, "word": " الـ", "probability": 0.6263427734375}, {"start": 970.55, "end": 970.71, "word": " F", "probability": 0.94140625}, {"start": 970.71, "end": 970.83, "word": " is", "probability": 0.52783203125}, {"start": 970.83, "end": 971.41, "word": " differentiable", "probability": 0.90576171875}, {"start": 971.41, "end": 971.75, "word": " عليها", "probability": 0.983642578125}, {"start": 971.75, "end": 972.05, "word": " مادام", "probability": 0.55908203125}, {"start": 972.05, "end": 972.79, "word": " differentiable", "probability": 0.810546875}, {"start": 972.79, "end": 973.31, "word": " إذا", "probability": 0.751220703125}, {"start": 973.31, "end": 973.97, "word": " continuous", "probability": 0.8564453125}, {"start": 973.97, 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X2 يعني موجودة في الـ I اللي هي لإن هذي جزئية من مين من I there exist C such that F prime of C بساوي F of X1 أو F of X2 ناقص", "tokens": [28814, 15730, 13412, 32887, 9566, 2423, 39184, 12302, 39352, 440, 37956, 3714, 6027, 11296, 44650, 5016, 4587, 28671, 11933, 15730, 456, 2514, 550, 456, 2514, 383, 6055, 29399, 2304, 1829, 30731, 27188, 2655, 25720, 1783, 16, 4032, 1783, 17, 37495, 22653, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 286, 13672, 1829, 39896, 5296, 28814, 1863, 8032, 8848, 1829, 10874, 11622, 19986, 10632, 9154, 3714, 9957, 9154, 286, 456, 2514, 383, 1270, 300, 479, 5835, 295, 383, 4724, 3794, 995, 45865, 479, 295, 1783, 16, 34051, 479, 295, 1783, 17, 8717, 995, 4587, 9381], "avg_logprob": -0.25847739773861905, "compression_ratio": 1.444954128440367, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 977.94, "end": 978.28, "word": "إذا", "probability": 0.6904296875}, {"start": 978.28, "end": 978.98, "word": " شروط", "probability": 0.7991536458333334}, 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تكعيب بالشكل هذا هذا الان strictly ايه شمالها decreasing هذه F is strictly decreasing", "tokens": [3555, 3794, 995, 2407, 8608, 6027, 3555, 1783, 6055, 4117, 3615, 1829, 3555, 23758, 32748, 6027, 3660, 23758, 32748, 6027, 3660, 44945, 25957, 1211, 1895, 260, 655, 50113, 1211, 479, 295, 1783, 8608, 995, 2407, 8608, 6027, 3555, 1783, 6055, 4117, 3615, 1829, 3555, 20666, 8592, 28820, 23758, 23758, 2423, 7649, 20792, 1975, 1829, 3224, 13412, 2304, 6027, 11296, 23223, 29538, 479, 307, 20792, 23223], "avg_logprob": -0.3001893943909443, "compression_ratio": 1.6689655172413793, "no_speech_prob": 6.377696990966797e-06, "words": [{"start": 1415.22, "end": 1415.74, "word": "بساو", "probability": 0.733154296875}, {"start": 1415.74, "end": 1416.28, "word": " سالب", "probability": 0.70751953125}, {"start": 1416.28, "end": 1416.52, "word": " X", "probability": 0.6630859375}, {"start": 1416.52, "end": 1417.12, "word": " تكعيب", "probability": 0.92978515625}, {"start": 1417.12, "end": 1417.96, "word": 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شرط الدال ال derivative من موجب إلى سلب local maximum هذه النقاط اللى احنا اخدناه م�� النظرية السابقة طبعا بنحكي عن ال interior points و F", "tokens": [5172, 9381, 9640, 43242, 7578, 6024, 48506, 35186, 10874, 15042, 27884, 13672, 7578, 31439, 2423, 1500, 16712, 5016, 12610, 13412, 2288, 9566, 32748, 6027, 2423, 13760, 9154, 3714, 29245, 3555, 30731, 8608, 46152, 2654, 6674, 29538, 28239, 4587, 41193, 13672, 7578, 1975, 5016, 8315, 1975, 9778, 3215, 8315, 3224, 9154, 28239, 19913, 2288, 10632, 21136, 16758, 28671, 23032, 3555, 3615, 995, 44945, 5016, 4117, 1829, 18871, 2423, 10636, 2793, 4032, 479], "avg_logprob": -0.20920139302810034, "compression_ratio": 1.4747474747474747, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2283.61, "end": 2284.07, "word": "فصار", "probability": 0.6953938802083334}, {"start": 2284.07, "end": 2284.45, "word": " عندى", "probability": 0.884033203125}, {"start": 2284.45, "end": 2284.71, "word": " الآن", "probability": 0.6773681640625}, 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95, "seek": 234478, "start": 2329.44, "end": 2344.78, "text": "نجرها بس من عندنا هنا هي اللي قلته بس نجرها من النظرية let f be continuous on the interval a و b إذا إيش مخصر دين إن ال function is continuous على فترة a و b و ناخد c عبارة عن interior point لمين", "tokens": [1863, 7435, 2288, 11296, 4724, 3794, 9154, 43242, 8315, 34105, 39896, 13672, 1829, 12174, 1211, 47395, 4724, 3794, 8717, 7435, 2288, 11296, 9154, 28239, 19913, 2288, 10632, 718, 283, 312, 10957, 322, 264, 15035, 257, 4032, 272, 11933, 15730, 11933, 1829, 8592, 3714, 9778, 9381, 2288, 11778, 9957, 36145, 2423, 2445, 307, 10957, 15844, 6156, 2655, 25720, 257, 4032, 272, 4032, 8717, 47283, 3215, 269, 6225, 3555, 9640, 3660, 18871, 10636, 935, 32767, 9957], "avg_logprob": -0.3145833277702332, "compression_ratio": 1.5053763440860215, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2329.44, "end": 2330.0, "word": "نجرها", "probability": 0.609130859375}, {"start": 2330.0, "end": 2330.22, "word": " بس", 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{"start": 2586.0, "end": 2587.54, "word": " المتحققات", "probability": 0.9727376302083334}, {"start": 2587.54, "end": 2587.74, "word": " على", "probability": 0.80078125}, {"start": 2587.74, "end": 2588.06, "word": " هذه", "probability": 0.9248046875}, {"start": 2588.06, "end": 2588.74, "word": " الفترة", "probability": 0.9679361979166666}, {"start": 2588.74, "end": 2589.5, "word": " لمين؟", "probability": 0.92919921875}], "temperature": 1.0}, {"id": 106, "seek": 261727, "start": 2589.89, "end": 2617.27, "text": "للـ Mean Value Theorem إذا نطبق الـ Mean Value Theorem على هذا الانترال لكي نحصل على ذلك اللي هو F there exist CX element in X وC such that F of CX فبرايم of CX بساوي F of C ناقص", "tokens": [1211, 1211, 39184, 12302, 39352, 440, 37956, 11933, 15730, 8717, 9566, 3555, 4587, 2423, 39184, 12302, 39352, 440, 37956, 15844, 23758, 2423, 7649, 2655, 2288, 6027, 5296, 4117, 1829, 8717, 5016, 36520, 15844, 29910, 23275, 13672, 1829, 31439, 479, 456, 2514, 383, 55, 4478, 294, 1783, 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"end": 3410.9, "word": " اللي", "probability": 0.959716796875}, {"start": 3410.9, "end": 3411.34, "word": " هنخد", "probability": 0.7601318359375}, {"start": 3411.34, "end": 3411.84, "word": " الآن", "probability": 0.6666259765625}, {"start": 3411.84, "end": 3412.68, "word": " for", "probability": 0.63037109375}], "temperature": 1.0}, {"id": 138, "seek": 344304, "start": 3413.66, "end": 3443.04, "text": "x أكبر من 100 من 0 بدنا نعمل application أو we apply the mean value theorem on the interval 0,100 أو x نظرا نتحقق الشروط بيكون عند there exist c element in 0,x such that f prime of c بيساوي f of x ناقص f of 0 على x minus 0", "tokens": [87, 5551, 4117, 26890, 9154, 2319, 9154, 1958, 47525, 8315, 8717, 25957, 1211, 3861, 34051, 321, 3079, 264, 914, 2158, 20904, 322, 264, 15035, 1958, 11, 6879, 34051, 2031, 8717, 19913, 23557, 8717, 2655, 5016, 4587, 4587, 25124, 32887, 9566, 4724, 1829, 30544, 43242, 456, 2514, 269, 4478, 294, 1958, 11, 87, 1270, 300, 283, 5835, 295, 269, 4724, 1829, 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3460.05, "end": 3460.35, "word": " Sin", "probability": 0.76953125}, {"start": 3460.35, "end": 3460.91, "word": " X", "probability": 0.9931640625}, {"start": 3460.91, "end": 3462.23, "word": " بيساوي", "probability": 0.80458984375}, {"start": 3462.23, "end": 3462.75, "word": " X", "probability": 0.98193359375}, {"start": 3462.75, "end": 3463.49, "word": " في", "probability": 0.70263671875}, {"start": 3463.49, "end": 3463.95, "word": " Cos", "probability": 0.96142578125}, {"start": 3463.95, "end": 3464.53, "word": " C", "probability": 0.96435546875}, {"start": 3464.53, "end": 3465.87, "word": " لكن", "probability": 0.9365234375}, {"start": 3465.87, "end": 3466.33, "word": " الآن", "probability": 0.6158447265625}, {"start": 3466.33, "end": 3466.57, "word": " أنا", "probability": 0.62451171875}, {"start": 3466.57, "end": 3466.87, "word": " عندي", "probability": 0.79833984375}, {"start": 3466.87, "end": 3467.33, "word": " Cos", "probability": 0.9453125}, {"start": 3467.33, "end": 3467.99, 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