Using graphic method, find the value of y when x = 38 from the following data:

x	10	20	30	40	50	60
y	63	55	44	34	29	22

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

By constructing a difference table and using the second order differences as constant, find the sixth term of the series 8,12,19,29,42…

Prove that f(4) = f(3) + Δf(2) + Δ² f(1) + Δ³ f(1) taking ‘1’ as the interval of differencing.

Given U₀ = 1, U₁ = 11, U₂ = 21, U₃ = 28 and U₄ = 29 find Δ⁴U₀

Given y₃ = 2, y₄ = −6, y₅ = 8, y₆ = 9 and y₇ = 17 Calculate Δ⁴y₃

From the following table find the missing value

x	2	3	4	5	6
f(x)	45.0	49.2	54.1	-	67.4

Evaluate ∆(log ax).

If y = x³ − x² + x − 1 calculate the values of y for x = 0,1,2,3,4,5 and form the forward differences table.

If h = 1 then prove that (E⁻¹Δ)x³ = 3x² − 3x + 1.

If f(x) = x² + 3x then show that Δf(x) = 2x + 4

Find the missing entry in the following table

x	0	1	2	3	4
yx	1	3	9	-	81

Following are the population of a district

Year (x)	1881	1891	1901	1911	1921	1931
Population (y) Thousands	363	391	421	-	467	501

Find the Population of the year 1911.

Using graphic method, find the value of y when x = 48 from the following data:

x	40	50	60	70
y	6.2	7.2	9.1	12

The following data relates to indirect labour expenses and the level of output

Months	Jan	Feb	Mar	Apr	May	June
Units of output	200	300	400	640	540	580
Indirect labour expenses (Rs)	2500	2800	3100	3820	3220	3640

Estimate the expenses at a level of output of 350 units, by using graphic method

A second degree polynomial passes though the point (1,-1) (2,-1) (3,1) (4,5). Find the polynomial.