Δ²y₀ = _______.

(a)

y₂ −2y₁ + y₀

(b)

y₂ + 2y₁ − y₀

(c)

y₂ + 2y₁ + y₀

(d)

y₂ + y₁ + 2y₀

If ‘n’ is a positive integer Δⁿ[ Δ^-n​ ​​​​​​f(x)] _______.

(a)

f(2x)

(b)

f(x+ h)

(c)

f (x)

(d)

Δf(x)

∇ f(a) = _______.

(a)

f (a) + f(a−h)

(b)

f (a) − f(a + h)

(c)

f (a) − f(a − h)

(d)

f (a)

Lagrange’s interpolation formula can be used for _______.

(a)

equal intervals only

(b)

unequal intervals only

(c)

both equal and unequal intervals

(d)

none of these.

If f (x)=x²  + 2x + 2 and the interval of differencing is unity then Δf (x) _______.

(a)

2x −3

(b)

2x +3

(c)

x + 3

(d)

x − 3

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

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.

Evaluate \({ \Delta }^{ 2 }\left( \frac { 1 }{ x } \right) \) by taking ‘1’ as the interval of differencing.

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

Estimate the production for 1964 and 1966 from the following data

Year	1961	1962	1963	1964	1965	1966	1967
Production	200	220	260	-	350	-	430

The values of y = f(x) for x = 0,1,2, ...,6 are given by

x	0	1	2	3	4	5	6
y	2	4	10	16	20	24	38

Estimate the value of y (3.2) using forward interpolation formula by choosing the four values that will give the best approximation.

Using appropriate interpolation formula find the number of students whose weight is between 60 and 70 from the data given below

Weight in lbs	0-40	40-60	60-80	80-100	100-120
No.of.students	250	120	100	70	50