Question

From the following table obtain a polynomial of degree y in x

x	1	2	3	4	5
y	1	-1	1	-1	1

Answer 1

To find a polynomial y = f(x) 

Here x₀ = 1, h = 1

x = x + nh x = 1 + n(1) n = x – 1 

We find the forward differences as below

Using Newton’s forward interpolation formula,