| By Secant | Example2 | |||||||||||||||
| ¦(x) = e–x – e–2x + 1 | التعويض | f(x) | |xn+1 − xn | | النسبة المئوية |
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| n | xi-1 = قيمة افتراضية ® | 0 | 1.0000 | |||||||||||||
| 0 | xi = قيمة افتراضية ®x1 = | -1 | -3.6708 | │ϵα│ | ||||||||||||
| 1 | Secant law®x2 = | -0.21409727 | 0.7043 | 0.7859 | 367.0774 | |||||||||||
| 2 | ®x3 = | -0.34060574 | 0.4295 | 0.1265 | 37.1422 | |||||||||||
| 3 | ®x4 = | -0.53839609 | -0.2220 | 0.1978 | 36.7370 | |||||||||||
| 4 | ®x5 = | -0.47100316 | 0.0365 | 0.0674 | 14.3084 | |||||||||||
| 5 | ®x6 = | -0.48051421 | 0.0025 | 0.0095 | 1.9793 | |||||||||||
| 6 | ®x7 = | -0.48122059 | 0.0000 | 0.0007 | 0.1468 | |||||||||||
| 7 | ®x8 = | -0.48121182 | 0.0000 | 0.0000 | 0.0018 | |||||||||||
| 8 | ®x9 = | -0.48121183 | 0.0000 | 0.0000 | 0.0000 | |||||||||||
| 9 | ®x10 = | -0.48121183 | 0.0000 | 0.0000 | 0.0000 | |||||||||||
| stop because the last two answers has been Equaled | تساوت نسبتين ¬ المقدم : (المقدم - التالي) للنسبة الأولى = المقدم : (المقدم - التالي) للنسبة الثانية | |||||||||||||||
| By Newton | To: Example 9 | البرهان:ـ | ||||||||||||||
| ¦(x) = e–x – e–2x + 1 | المشتقة الأولى | الدالة / المشتقة | x(i+1) القيمة الجديدة |
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| x(i) | f x(i) | f¯x(i) | fx(i)/f¯x(i) | x(i)−fx(i)/f¯x(i) | ||||||||||||
| 0.2 | 1.148410707 | 0.52190934 | 2.200403 | -2.00040268 | ||||||||||||
| -2.0004026777 | -46.25010655 | 101.89224521 | -0.453912 | -1.54649074 | ||||||||||||
| -1.5464907391 | -16.34773455 | 39.39043448 | -0.415018 | -1.13147286 | ||||||||||||
| -1.1314728606 | -5.511140565 | 16.12250046 | -0.341829 | -0.78964371 | ||||||||||||
| -0.7896437146 | -1.648886015 | 7.50038356 | -0.219840 | -0.56980349 | ||||||||||||
| -0.5698034887 | -0.357620115 | 4.48315983 | -0.079770 | -0.49003383 | ||||||||||||
| -0.4900338333 | -0.032265095 | 3.69690164 | -0.008728 | -0.48130623 | ||||||||||||
| -0.4813062288 | -0.000341596 | 3.61886994 | -0.000094 | -0.48121184 | ||||||||||||
| -0.4812118360 | -3.94505E-08 | 3.61803409 | 0.000000 | -0.48121183 | ||||||||||||
| -0.48121183 | 0 | 3.61803399 | 0.000000 | -0.48121183 | ||||||||||||
| stop because the last two answers has been Equaled | ||||||||||||||||