! " # $# % & # ' # % ( " ) # # " * # + ) $$) " &) * ) $# % # "' $# # ,# $! -./) /0 # /% - Qi,j (x) = (x − xi−j )Qi,j−1 (x) − (x − xi )Qi−1,j−1(x) xi − xi−j /0% 1 - Pn (x) = f [x0 ] + n f [x0 , x1 , · · · , xk ](x − x0 )(x − x1 ) · · · (x − xk−1 ) k=1 1 - Pn (x) = f (x0 ) + n s k=1 k Δk f (x0 ) - 1 - Pn (x) =P2m+1 (x) = f (x0 ) + sh (f [x−1 , x0 ] + f [x0 , x1 ]) + s2 h2 f [x−1 , x0 , x1 ] 2 s(s2 − 1)h3 (f [x−2 , x−1 , x0 , x1 ] + f [x−1 , x0 , x1 , x2 ]) + 2 + · · · + s2 (s2 − 1)(s2 − 4) · · · (s2 − (m − 1)2 )h2m f [x−m , · · · , xm ] s(s2 − 1) · · · (s2 − m2 )h2m+1 (f [x−m−1 , . . . , xm ] + f [x−m , · · · , xm+1 ]) + 2 2 1 - n k −s Pn (x) = f (xn ) + (−1) ∇k f (xn ) k k=1 1 1 f (x0 ) = f (x0 + h) − f (x0 ) h − f (ξ) h 2 3'. 4' 1 1 h2 [−3f (x0 ) + 4f (x0 + h) − f (x0 + 2h)] + f (ξ) 2h 3 3'. 5 1 f (x0 ) = 1 h2 [f (x0 + h) − f (x0 − h)] − f (ξ) 2h 6 /%. 5 1 f (x0 ) = 1 h4 [f (x0 − 2h) − 8f (x0 − h) + 8f (x0 + h) − f (x0 + 2h)] + f (v) (ξ) 12h 30 /%. 4' 1 f (x0 ) = 1 h4 [−25f (x0 ) + 48f (x0 + h) − 36f (x0 + 2h) + 16f (x0 + 3h) − 3f (x0 + 4h)] + f (v) (ξ) 12h 5 & ' 5 1 f (x0 ) = 1 h2 (iv) [f (x − h) − 2f (x ) + f (x + h)] − f (ξ) 0 0 0 h2 12 6$ 7# 1 h h 1 Nj (h) = Nj−1 + j−1 Nj−1 − Nj−1 (h) 2 2 −1 2 f (x0 ) = 15 f (3) 8.9 " % " % " % i xi Qi,0 0 Qi,1 1 3 a 1.828 b 2 √ 1.707 1.747 c 1.764 1.726 1.737 8 8 : 5 Qi,2 Qi,3 / )0 a! b c ) # Qi,4 1.691 20 % " xi f (xi ) 0.0 0.2 0.4 0.6 0.8 1 1.2214 1.4918 1.8221 2.2255 f (0.1) f (0.7) ; 1! ; - 1 ; 2 1 $) % #"! "# % 8 [0, 2] f (x) * S(x) " # # 0≤x≤1 1 + 2x − x3 , S(x) = 2 3 2 + b(x − 1) + c(x − 1) + d(x − 1) , 1 ≤ x ≤ 2 % )0 b! c d " : 15 15 % " xi −0.92 f (xi ) 84.64 −0.86 −0.84 73.96 70.56 −0.78 60.84 −0.74 −0.72 54.76 51.84 −0.66 43.56 f (−0.84) f (−0.78) % #" ' ) "#! % < 15 f (x) = xe2x * f (0.5) h = 0.01 " % # % $ ' " " = 20 h > 0 ' * * f (x0 + h) − f (x0 ) h h2 f (x0 ) = − f (x0 ) − f (x0 ) + O(h3 ) h 2 6 * " / )0 f (x) = ln x · tan x * x0 = 3 . h = 0.4 * * O(h3 ) % " >