Question

Find the polynomial for the following data by Newton's backward
difference formula
x 0 1 2 3
y 3 2 9 18​

Answer 1

Answer:

I cannot understand the question because I don't know the formula of this question

Answer 2

Step-by-step explanation:

Here x0 = 10, x1 = 30, x2 = 50, h= x1 - x0 = 30 - 10 = 20, y0 = 42, y1 = 64, y2 = 88

Linear Interpolation:

64 - 42 / 30 - 10

Quadratic Interpolation

y΄ (x0) = ( -3y0 + 4 y1 – y2 ) /(2h) = [ -3(42) + 4 (64) – 88 ] /40 = 1.05

y΄ (x1) = (y2 - y0 ) /(2h) = (88 - 42 ) / 40 = 1.15

y΄ (x2) = ( y0 - 4 y1 + 3 y2 ) /(2h) = ( 42 - 256 + 264 ) / 40 = 1.25

y΄΄(x0) = ( y0 -2 y1 + y2 ) /(2h) = ( 42 - 128 + 88 ) / 40 = 0.05