Δf(x) = _______.

(a)

f(x+ h)

(b)

f(x) − f(x+h)

(c)

f(x + h) − f(x)

(d)

f (x) − f(x−h)

If m and n are positive integers then Δ^mΔⁿf(x) = _______.

(a)

Δ^m+nf (x)

(b)

Δ^mf(x)

(c)

Δⁿf (x)

(d)

Δ^m-nf (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

E².f(x) = ______________

(a)

f(x + h)

(b)

f(x + 2h)

(c)

f(2h)

(d)

f(2x)

If c is a constant, then Δc.f(x) ______________

(a)

0

(b)

c.f(Δx)

(c)

c.Δf(x)

(d)

f(Δcx)

Δ[f{x) . g(x)] = __________

(a)

Δf(x). Δg(x)

(b)

f(x) . Δg(x) + g(x) .Δf(x)

(c)

f(x) . Δg(x)

(d)

f(Δx) . g(Δx)

E^-nf(x) is ______________

(a)

F(x + nh)

(b)

F(x - nh)

(c)

F(-nh)

(d)

f(x - n)

(1 + Δ) (1 - ∇) is ______________

(a)

0

(b)

1

(c)

-1

(d)

(1 - ∇ . Δ)

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

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

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

Evaluate \(\Delta \)\(\left[ \frac { 5x+12 }{ { x }^{ 2 }+5x+6 } \right] \) by taking ‘1’ as the interval of differencing.

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

Find y when x = 0.2 given that

x	0	1	2	3	4
y	176	185	194	202	212

If y₇₅ = 2459, y₅₀ = 2018, y₈₅ = 1180, and y₉₀ =402, find y₈₂

x	75	80	85	90
y	2459	2018	1180	402

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.

From the following table, estimate the premium for a policy maturing at the age of 58.

Age (x)	40	45	50	55	60
Premium (y)	114.84	96.16	83.32	74.48	68.48

Using Lagrange's formula find the value of y when x = 4 from the following table.

x	0	3	5	6	8
y	276	460	414	343	110