L oa £B^ , , P J 1 Cl
b) TnX^ng hg»p k= J.
?:u5t phat tú x^, te x^y c^vng cac phSn tii :
(2.19) x^ = x^ Y ' ' ^ ' ^ ' ' x§ = 2 x ! ? - x ^ x | : ^ 2 . | - x f ; .
Í^P ty s a l p'^^dn suy rgng b^v^c ba Ăx2, xiz^^^ ^^ ỵ \ ^j ) :
(2.20) Ăx?, x | . x ° , x ° ; f ) ^ , ( x ? ) . 1 , ( 4 ) f . ( x p = = Ăx?, x ° , x , ° ; ^ ) ^ - , ( x 5 ) f , , ( x ° ) - = Ăx?, x ° , x , ° ; ^ ) ^ - , ( x 5 ) f , , ( x ° ) -
- A ( x ° , xjf. x ^ ; f ) ^ ! i ( x S ) ^ ^ ( a | J .
Dv^a x-ao ( 1 . 1 ) , ( 1 . 3 ) tú (2.20) ta cuy ra :
( 2 . 2 1 ) Ax| = Ax^ + ĂxS, y°i(f) f , (x°) +
+ A ( 4 , x ° , x ^ f ) f . ( x ? ) </ 2(x?) + + Ăx°. x ° , x ? , x ° ; f ) ^ / ^ ( 4 ) . | 1 , ( x p . 7 1 . ( 4 ) + Ăx°. x ° , x ? , x ° ; f ) ^ / ^ ( 4 ) . | 1 , ( x p . 7 1 . ( 4 )
+ A ( x | , 2c°;<f) Cf.^hX') ^ A ( x ° , x ° ; f ) f / x ^ ^ ) -
- A ( x ° , x ° ; ^ ) ^ / , ( x ' ^ ) f A ( 4 , x ^ , x^; f ) f ^ ( x ? ; ) f 2 ( ^ - ^
+ Ăx;;. x^, .4, x'^f )f^(xp f^(xp V 2^^-
Dya vao ( I . I ) S1 Oiúóng T v u T l . l ) f> ( 2 . 2 1 ) euy ra s
( 2 . 2 2 ) Axe = Ax^^ + A ( 4 , ^ , ^ ) ^^ ..(zX^, x^) ( ^ - x^) ^
+ A ( x | , x ^ , x ° ; j ) / : . / . , ( x ? ) y o ( x p + Y ^ ( x ° ) ^ 2 ( ^ ° > - 7 + ^ A ( x | . x | , X?, x ^ f ) . , ^ ^ ( x ° ) ^ - . l ( x p f 2 ( ^ 3 > -
DoV each d ^ t ( 2 . 1 9 ) , t a co t h e chfn diT^'c a $ t h^ ham ( c b a r ^ hpn 6^j_Cx) = (x - X.;) scio cho : ( 2 . 2 5 ) Ăx^, x:?, x ^ ' j ) /fy , ( x ? ) < / 2 ( x 5 ) ^ ^ , ( X ' ^ ) Y ' 2 ( X ° ) 7 = 0 Ăx9, 4 , x ? , x " ; f ) ^ o ( 4 ^ ' / l ( ^ ) V 2 ( x p = 2 ^ A r^o 0 ...0 . . 0 . ^ ^ I j / _ o o > 2 . , ' Tl / 0 Ô . _ / O -•'\ / '-^ 0 \ / O O N t r o n g cro j | ( x j - x ^ ; : = U ^ - :^:c;'^ ^^5 " ^r '•^^^ - ^ ^ ) * Di^a vao ( 2 . 2 5 ) t v ( 2 . 2 2 ) t a nhdn :
( 2 . 2 4 ) Ax^ - Ax^ + Ă:c?, 4 * , ^ ) f , ( x j , x^^) (x? - x^) ^
+ A ( x 5 . 4 , X?, x ^ ; p (x^ - x ^ ) ( x ^ - ^ ) ( x ^ - x ^ )
H ^ t k h a c , l ^ p t y s a i p^an t o n g q u a t su^- rgng Ăx,X2, 'r^, x ^ ; ^ ) ,
t r o n g d6 X = Xj i- ^ ^ , l y l u ^ n hoan t o a n trc^ng t v n^ú trOn t a nh&n.
(2.25) Ax - Ax° > A ( 4 , X?; f ) f^(x, x°) (x - x^) ^ ^ A ( 4 . x°, x°}f ) / : y i ( ^ ) ^ 2 ^ ^ ) ^ f l ^ ^ ° > f 2 ( ^ ° > - 7 ^ ^ A ( 4 . x°, x°}f ) / : y i ( ^ ) ^ 2 ^ ^ ) ^ f l ^ ^ ° > f 2 ( ^ ° > - 7 ^ + Ăx, x°, X?. x°; f ) ^Q(x)f,,(x) V'2^^^' ThS nhttog : (2.26) T f i ( x . x°) - f^(x^, x ° ) 7 ( x - x ° ) = = f ^ ( x , x^, x°) (x - x ° ) (x - x p . L5y (2.26) thoy vao (2.25) ta nh§n t
(2.27) Ax = Ax°+ Ăx|, x°j ^ ) ^^Uy x*^) (x - 3°) +
+ Ă3^, x°; J ) ^ ^ ( x , x^, x°) (x - x°) (x - xp *
+ A ( 4 , X?. x ^ f ) r f i ( x ) ^ ' ' 2 ( ^ ) + Y l ( x ° ) y 2 ( x ° ) 7 +
•KĂx, 4 , x°, x ° 5 f ) f o ( x ) f ^ ( x ) f 2 ( x ) . D\?a vao (2,24) va (2.27) ta thgy re-ng vol Vx 6iXlst j D\?a vao (2,24) va (2.27) ta thgy re-ng vol Vx 6iXlst j
trong d6 :
^^'^tl = 1 x s / / A ( a ^ , 4 i f ) ^ ^ ( x , x ° , x°) ( x - x ° ) I J ^.
+ A ( x | , x ° , x ° » f ) ^ f ^ ( x ) f2(=^)- f . C x ° ) f 2 ( ^ ° ) 7 / - ^ 2 2 2 2
^//Ăx. 4,3c?, x^iy )//rn //x^^//.n ^f.u)//jl
1 = 0 •*• i==o ' ^