Answer to Question #55523 in Quantitative Methods for Joseph

Question

8 The zeroeth divided difference of the function f, with respect to
x i
, denoted by
f[x i ]
is the same as



f[x i ]=f(x i )



f[x 0 ]=f(x i )



f[x]=f(x i )



f[x]=f(xi)





9 The quantity
L 0 (x)
of the Lagrange’s interpolating polynomial P(x) is equal to



(x−x 1 )(x−x 2 )(x−x 3 )(x 0 −x 1 )(x 0 −x 2 )(x 0 −x 3 )



(x−x 1 )(x1−x 2 )(x 0 −x 3 )(x 0 −x 1 )(x 0 −x 2 )(x 0 −x 3 )



(x−x 1 )(x−x 2 )(x−x 3 )(x−x 1 )(x−x 2 )(x−x 3 )



(x−x 1 )(x−x 0 )(x−x 3 )(x 0 −x 4 )(x 0 −x 2 )(x 0 −x 3 )





10 A square matrix is called ………….. if all the elements above the main diagonal vanish.

upper triangular
triangular

lower triangular

rectangular