Construct a forward difference table for the following data

x	0	10	20	30
y	0	0.174	0.347	0.518

Construct a forward difference table for y = f(x) = x³+2x+1 for x = 1,2,3,4,5

Using interpolation estimate the business done in 1985 from the following data

Year	1982	1983	1984	1986
Business done (in lakhs)	150	235	365	525

Using interpolation, find the value of f(x) when x = 15

x	3	7	11	19
f(x)	42	43	47	60

Find the missing figures in the following table

x	0	5	10	15	20	25
y	7	11	-	18	-	32

Find f(0.5) if f(−1) = 202, f (0)= 175, f(1) = 82 and f(2) = 55

Using Lagrange’s interpolation formula find a polynomial which passes through the points (0, –12), (1, 0), (3, 6) and (4,12).

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

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

From the following data find y at x = 43 and x = 84

x	40	50	60	70	80	90
y	184	204	226	250	276	304

The area A of circle of diameter ‘d’ is given for the following values

D	80	85	90	95	100
A	5026	5674	6362	7088	7854

Find the approximate values for the areas of circles of diameter 82 and 91 respectively 

Find the missing term from the following data.

x	20	30	40
y	51	-	34

If f(0) = 5, f(1) = 6, f(3) = 50, find f(2) by using Lagrange's formula.

Find the missing term from the following data

x	1	2	3	4
f(x)	100	-	126	157

When h = 1, find Δ (x³).

Find the second order backward differences of f(x).