ЛЕКЦІЇ ² ВПРАВИ

Çàñòîñîâóþ÷è (n + 1) ðàç³â ôîðìóëó Êîø³ ³ âðàõîâóþ÷è
âëàñòèâîñò³ (7.15.11), ìàòèìåìî
Rn( x)
Rn( x) − Rn( x0)
R′
n( c1)
+ 1 + 1
( x−x0)
( x− x0)
( n+ 1)( x−x0)
′ ( 1) − ′ ( 0)
′′( 2)
n
n−1
( n+ 1)( x− x ) ( n+ 1) n( x−x
)
= = =
n n n
( n+
1 )
n n n n ()
R c R x R c R c
= = = ... = .
1!
0 0
( n + )
(7.15.13)
Ó ôîðìóë³ (7.15.13) ñòàë³ c 1 , c 2 , ..., c n , c — íåâ³äîì³, àëå
çã³äíî ç òåîðåìîþ Êîø³ ìè çíàºìî, ùî âñ³ âîíè çíàõîäÿòüñÿ
ì³æ õ ³ õ 0 . ßêùî x > x 0 , òî öåé ôàêò, íàïðèêëàä äëÿ ñ,
ìîæíà çàïèñàòè òàê:
ñ = x 0 + θ(x – x 0 ), 0 < θ