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314.69, "end": 327.49, "text": "الآن لو جيت انا E أُس R إذا الـ E أُس R هي عبارة عن الـ exponential of R إذا الـ E لو أرفعها لأي عدد", "tokens": [6027, 148, 48506, 45164, 10874, 36081, 1975, 8315, 462, 5551, 10859, 3794, 497, 11933, 15730, 2423, 39184, 462, 5551, 10859, 3794, 497, 39896, 6225, 3555, 9640, 3660, 18871, 2423, 39184, 21510, 295, 497, 11933, 15730, 2423, 39184, 462, 45164, 5551, 28480, 3615, 11296, 5296, 10721, 1829, 6225, 3215, 3215], "avg_logprob": -0.3043749862909317, "compression_ratio": 1.278688524590164, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 314.69, "end": 315.29, "word": "الآن", "probability": 0.4573567708333333}, {"start": 315.29, "end": 315.59, "word": " لو", "probability": 0.50146484375}, {"start": 315.59, "end": 315.95, "word": " جيت", "probability": 0.7470703125}, {"start": 315.95, "end": 316.65, "word": " انا", "probability": 0.75927734375}, {"start": 316.65, "end": 318.37, "word": " E", "probability": 0.52587890625}, {"start": 318.37, "end": 318.69, "word": " أُس", "probability": 0.5751953125}, {"start": 318.69, "end": 318.95, "word": " R", "probability": 0.93603515625}, {"start": 318.95, "end": 319.25, "word": " إذا", "probability": 0.57080078125}, {"start": 319.25, "end": 319.55, "word": " الـ", "probability": 0.5853271484375}, {"start": 319.55, "end": 319.67, "word": " E", "probability": 0.9130859375}, {"start": 319.67, "end": 319.95, "word": " أُس", "probability": 0.9767252604166666}, {"start": 319.95, "end": 320.25, "word": " R", "probability": 0.95068359375}, {"start": 320.25, "end": 320.55, "word": " هي", "probability": 0.92236328125}, {"start": 320.55, "end": 320.91, "word": " عبارة", "probability": 0.9063720703125}, {"start": 320.91, "end": 321.07, "word": " عن", "probability": 0.994140625}, {"start": 321.07, "end": 321.17, "word": " الـ", "probability": 0.800048828125}, {"start": 321.17, "end": 321.65, "word": " exponential", "probability": 0.63525390625}, {"start": 321.65, "end": 322.05, "word": " of", "probability": 0.9228515625}, {"start": 322.05, "end": 322.35, "word": " R", "probability": 0.9833984375}, {"start": 322.35, "end": 325.49, "word": " إذا", "probability": 0.718994140625}, {"start": 325.49, "end": 325.69, "word": " الـ", "probability": 0.74365234375}, {"start": 325.69, "end": 325.79, "word": " E", "probability": 0.94091796875}, {"start": 325.79, "end": 325.97, "word": " لو", "probability": 0.90673828125}, {"start": 325.97, "end": 326.65, "word": " أرفعها", "probability": 0.73321533203125}, {"start": 326.65, "end": 327.01, "word": " لأي", "probability": 0.94921875}, {"start": 327.01, "end": 327.49, "word": " عدد", "probability": 0.9835611979166666}], "temperature": 1.0}, {"id": 14, "seek": 34590, "start": 328.08, "end": 345.9, "text": "هي عبارة عن الـ E أُس R والتي أثبتناها من هنا E لأنها تساوي E exponential of واحد أشيل الواحد و أضع بدله أي متغير تظهر E أُس هذا المتغير وبالتالي ال exponential of R هي عبارة عن E أُس R وبالتالي أثبتنا هنا أن ال exponential هي شكل E", 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"probability": 0.974609375}, {"start": 342.42, "end": 342.68, "word": " R", "probability": 0.97900390625}, {"start": 342.68, "end": 343.28, "word": " وبالتالي", "probability": 0.95849609375}, {"start": 343.28, "end": 343.72, "word": " أثبتنا", "probability": 0.9923828125}, {"start": 343.72, "end": 343.88, "word": " هنا", "probability": 0.7041015625}, {"start": 343.88, "end": 344.12, "word": " أن", "probability": 0.54638671875}, {"start": 344.12, "end": 344.24, "word": " ال", "probability": 0.90576171875}, {"start": 344.24, "end": 344.68, "word": " exponential", "probability": 0.7197265625}, {"start": 344.68, "end": 345.12, "word": " هي", "probability": 0.95556640625}, {"start": 345.12, "end": 345.68, "word": " شكل", "probability": 0.7490234375}, {"start": 345.68, "end": 345.9, "word": " E", "probability": 0.9638671875}], "temperature": 1.0}, {"id": 15, "seek": 36216, "start": 349.18, "end": 362.16, "text": "فالـ Definition بقول لـ for every real number X we define the natural exponential function to be E أس X هي عبارة عن ال exponential of X الشرف اللي شرحناه قبل هي كان كله هذا كله إيه؟", "tokens": [5172, 6027, 39184, 46245, 849, 4724, 39648, 5296, 39184, 337, 633, 957, 1230, 1783, 321, 6964, 264, 3303, 21510, 2445, 281, 312, 462, 5551, 3794, 1783, 39896, 6225, 3555, 9640, 3660, 18871, 2423, 21510, 295, 1783, 25124, 28480, 13672, 1829, 13412, 2288, 5016, 8315, 3224, 12174, 36150, 39896, 25961, 28242, 3224, 23758, 28242, 3224, 11933, 1829, 3224, 22807], "avg_logprob": -0.36228812852148284, "compression_ratio": 1.3559322033898304, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 349.18, "end": 349.6, "word": "فالـ", "probability": 0.3973185221354167}, {"start": 349.6, "end": 350.34, "word": " Definition", "probability": 0.71533203125}, {"start": 350.34, "end": 350.62, "word": " بقول", "probability": 0.6724853515625}, {"start": 350.62, "end": 350.74, "word": " لـ", "probability": 0.48321533203125}, {"start": 350.74, "end": 350.94, "word": " for", 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"text": "ناقص ال bus E أُس 2 في تفاضل المقام تفاضل المقام E أُس 2X تفاضلها E أُس 2X في تفاضل الأُس 2 زي التفاضل اللي هو 1 على X وخلاص بنسيبها دلني هي كان مش ضروري أن بصرها", "tokens": [1863, 995, 4587, 9381, 2423, 1255, 462, 5551, 10859, 3794, 568, 8978, 6055, 5172, 46958, 1211, 9673, 4587, 10943, 6055, 5172, 46958, 1211, 9673, 4587, 10943, 462, 5551, 10859, 3794, 568, 55, 6055, 5172, 46958, 1211, 11296, 462, 5551, 10859, 3794, 568, 55, 8978, 6055, 5172, 46958, 1211, 16247, 10859, 3794, 568, 30767, 1829, 16712, 5172, 46958, 1211, 13672, 1829, 31439, 502, 15844, 1783, 4032, 9778, 1211, 33546, 44945, 3794, 1829, 3555, 11296, 11778, 1211, 22653, 39896, 25961, 37893, 48812, 2288, 13063, 1829, 14739, 4724, 9381, 2288, 11296], "avg_logprob": -0.3534058988764045, "compression_ratio": 1.832214765100671, "no_speech_prob": 1.6093254089355469e-06, "words": [{"start": 969.72, "end": 970.52, "word": "ناقص", "probability": 0.71270751953125}, {"start": 970.52, "end": 971.04, "word": " ال", 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987.91, "end": 1015.43, "text": "Example 3 F of X يساوي E أس X زائد X بقوللي show that F of X is one to one و بدنا نوجد تفاضل ال F inverse عند هذه النقطة أول شي سؤال ايه عشان أكبر ان ال F of X is one to one هدى أشوف هل هي increasing او decreasing طبعا هذه أول خطوة بنعملها انه بنشوف ال increasing و ال decreasing بنجيب F prime F prime تفاضل E أس X E أس X زائد تفاضل X اللى هو واحدة", "tokens": [11149, 335, 781, 805, 479, 295, 1783, 7251, 3794, 995, 45865, 462, 5551, 3794, 1783, 30767, 16373, 3215, 1783, 4724, 39648, 20292, 855, 300, 479, 295, 1783, 307, 472, 281, 472, 4032, 47525, 8315, 8717, 29245, 3215, 6055, 5172, 46958, 1211, 2423, 479, 17340, 43242, 29538, 28239, 47432, 3660, 5551, 12610, 44049, 8608, 33604, 6027, 1975, 1829, 3224, 6225, 8592, 7649, 5551, 4117, 3555, 2288, 16472, 2423, 479, 295, 1783, 307, 472, 281, 472, 8032, 3215, 7578, 5551, 8592, 38688, 8032, 1211, 39896, 5662, 1975, 2407, 23223, 23032, 3555, 3615, 995, 29538, 5551, 12610, 16490, 9566, 2407, 3660, 44945, 25957, 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{"start": 1310.25, "end": 1311.13, "word": " لكن", "probability": 0.876953125}, {"start": 1311.13, "end": 1311.43, "word": " هنا", "probability": 0.771484375}, {"start": 1311.43, "end": 1311.65, "word": " بدنا", "probability": 0.8583984375}, {"start": 1311.65, "end": 1311.93, "word": " نقوله", "probability": 0.9959309895833334}, {"start": 1311.93, "end": 1312.27, "word": " الآن", "probability": 0.81689453125}, {"start": 1312.27, "end": 1312.57, "word": " إيش", "probability": 0.724853515625}, {"start": 1312.57, "end": 1313.05, "word": " قوانين", "probability": 0.9884033203125}, {"start": 1313.05, "end": 1313.17, "word": " ال", "probability": 0.97802734375}, {"start": 1313.17, "end": 1313.65, "word": " exponential", "probability": 0.9326171875}, {"start": 1313.65, "end": 1314.21, "word": " function", "probability": 0.96484375}], "temperature": 1.0}, {"id": 56, "seek": 134219, "start": 1314.93, "end": 1342.19, "text": "For all numbers x وx وx1 وx2, the natural exponential e×x obeys the following laws. هي القوانين تبعت الـ exponential. e×x1 ضرب e×x2 في الضرب نقل تجمع الأسس. قاعدة حفظينها من زمان من المدرسة أن e×x1 ضرب e×x2 مدى مضربين ضرب إذا الأسس إياش نجمعه. e×x1 زاد x2", "tokens": [12587, 439, 3547, 2031, 4032, 87, 4032, 87, 16, 4032, 87, 17, 11, 264, 3303, 21510, 308, 37550, 87, 36346, 749, 264, 3480, 6064, 13, 39896, 25062, 2407, 7649, 9957, 6055, 3555, 34268, 2423, 39184, 21510, 13, 308, 37550, 87, 16, 48812, 25513, 308, 37550, 87, 17, 8978, 6024, 114, 25513, 8717, 4587, 1211, 6055, 7435, 2304, 3615, 16247, 3794, 3794, 13, 12174, 995, 22488, 3660, 11331, 5172, 19913, 9957, 11296, 9154, 30767, 2304, 7649, 9154, 9673, 3215, 2288, 3794, 3660, 14739, 308, 37550, 87, 16, 48812, 25513, 308, 37550, 87, 17, 3714, 3215, 7578, 3714, 11242, 25513, 9957, 48812, 25513, 11933, 15730, 16247, 3794, 3794, 11933, 1829, 33599, 8717, 7435, 2304, 3615, 3224, 13, 308, 37550, 87, 16, 30767, 18513, 2031, 17], "avg_logprob": -0.35887098023968356, "compression_ratio": 1.5291666666666666, 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obeys", "probability": 0.919189453125}, {"start": 1323.83, "end": 1324.05, "word": " the", "probability": 0.90234375}, {"start": 1324.05, "end": 1324.39, "word": " following", "probability": 0.5732421875}, {"start": 1324.39, "end": 1324.97, "word": " laws.", "probability": 0.319580078125}, {"start": 1325.47, "end": 1325.61, "word": " هي", "probability": 0.123046875}, {"start": 1325.61, "end": 1326.43, "word": " القوانين", "probability": 0.805267333984375}, {"start": 1326.43, "end": 1326.77, "word": " تبعت", "probability": 0.52734375}, {"start": 1326.77, "end": 1326.95, "word": " الـ", "probability": 0.657958984375}, {"start": 1326.95, "end": 1327.37, "word": " exponential.", "probability": 0.6474609375}, {"start": 1328.31, "end": 1329.13, "word": " e×x1", "probability": 0.763916015625}, {"start": 1329.13, "end": 1329.43, "word": " ضرب", "probability": 0.7257080078125}, {"start": 1329.43, "end": 1330.51, "word": " e×x2", "probability": 0.9814453125}, {"start": 1330.51, "end": 1330.69, 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