Oriental Renaissance: Innovative, educational, natural and social

Ключевые слова: строки, элементарные функции, предел, значение функции, интеграл, уравнение, формула Маклорена, формула Ньютона.
Annotation: The importance of Taylor's formula in solving mathematical problems in this article: the study of the distribution of elementary functions in series and its nature, the calculation of limits, finding the approximate value of a function at a given value, calculating integrals that cannot be related to elementary functions under integrals, differential issues such as solving equations using rows were studied. Keywords: Rows, elementary functions, limit, function value, integral,
equation, Macloren's formula, Newton's formula

KIRISH

Ingliz matematigi Bruk Teylor matematika faniga o’zining juda ko’p ilmiy ishlari bilan katta xissa qo’shgan olimlardan biridir. Uning matematika tarixida buyuk kashfiyotlaridan biri, o’zining 29 yoshida, ya’ni 1715 – yilda yaratgan nazariyasi

bilan matematika tarixida o’chmas iz qoldirdi. Bu kashfiyot nimadan iborat? Bizga funksiya berilgan bo’lsin. Mana shu funksiyani shunday ko’rinishidagi funksiya bilan yaqinlashtirish kerakki,
uning uchun

bo’lsin. Agar qator hadlarini yetarlicha katta olsak, u shunchalik funksiyaga yaqinlashadi.

B. Teylorning bu kashfiyoti “Methodus incrementorumdirecta et inversa” deb nomlanib, lotin tilida 1715 – yili yozildi. I. Nyuton va G. Leybnits Teylor zamondoshlari bo’lib, ular differensial va integral hisob asoschilari hisoblaydi. Teylor mana shu differensial va integral hisob asosida o’zining kashfiyotini amalga oshirdi.