Amaliy matematika va informatika ta’lim yo’nalishi 3-kurs talabalasi SULTONOV ERKINNING “ Hisoblash usullari “ fanidan 2-oraliq nazorat savollariga yozgan javobi
18-variant
1. Nyuton - Kottes formulalari.
2. Runge-Kutta metodlarning yaqinlashishi.
3. Integralning qiymatini 3 xona aniqlikda Trapetsiya, Simpson formulalari yordamida hisoblang.
Javoblari:
1.Nyuton - Kottes formulalari.
Berilgan y=f(x) funksiyaning aniq integrali
ni hisoblash talab qilingan bo’lsin.
O’zgarmas ![](data:image/png;base64,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) qadamni tanlab olib [a,b] kesmani teng uzoqlikdagi nuqtalar
yordamida n ta teng bo’lakka bo’lamiz va bu nuqtalarda f(x) funksiyaning qiymatlari
ma’lum bo’lsin.
1.Integral tagidagi y(x) funksiyani Lagranj interpolatsiyash ko’phadi ![](data:image/png;base64,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) bilan almashtirib , quyidagi taqribiy kvadratura formulasiga kelamiz
bunda ![](data:image/png;base64,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) biror-bir o’zgarmas koeffisiyentlar. Formula (1) dagi ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAWCAIAAABCPVsWAAAACXBIWXMAAA7GAAAOxAHY468QAAABEUlEQVR4nM2TPRKCMBCFwwxHCRaMJ8ATkMrK1i6UobGztLMhJelsrazkBHAChsLkLmsSFME/iJV0ZPblfW934wMAcv/8HzR/IlN8EaQVPUMeO8iKfVo5uxUJqSmNhHCRKb4TdCvDnUD1RaEYT5JpvvkZYlycEKqnuhm+TOZf6N7IWj7osKpGIjQGqfja8o1b9WVt04nX79/nntxkOpQYTNcOfFhqjo4rWTJ8k5lQUSZH+DArgT3cTKgqyg4DGtmYPel60m6bvtp6aVniBTZOGiSzO6QuIvZQkEVoKzE7ZMegmd2v9nOAlzn1cXr2dNnFmPpwipOIwk33O1GmLjWaL7HiXDIWOz1TQTy9eaWL23PaK/07f4cbCpm8AAAAAElFTkSuQmCC) koeffisiyentlar uchun aniq ifoda chiqaramiz . Ma’lumki,
bu yerda
![](data:image/png;base64,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)
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