Δ²y₀ = _______.

Δf(x) = _______.

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

E f (x)= _______.

∇ f(a) = _______.

Lagrange’s interpolation formula can be used for _______.

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

E²f(x) =
(a) E (E (f(x))
(b) E (f(x + h)
(c) f(x + 2h)
(d) F(x + h)

In the set of values f(x) = y, x is called
(a) independent variable
(b) dependent variable
(c) argument
(d) x - variable

∆⁴y₃=
(a) (E - 1)³y₃
(b) (E⁴ - 4E³ + 6E² - 4E + 1)y₃
(c) y₇ - 4y₆ + 6y₅ 4y₄ +y₃
(d) (E - 1)⁴y₃

(c) ∆f(x) = f(x + h) - f(x)
(b) Eⁿf(x) = f(x)
(c) ∇f(x) = f(x) - f(x - h)
(d) E.f(x) = f(x + h)

Using interpolation the polynomial which passes through the points (0,7), (5. 0), (3, 6) and (2, 5) is
(a) cubic polynomial
(b) a polynomial of degree 3
(c) linear polynomial
(d) y = ax³ + bx² + cx + d, a ≠ 0

The missing term in the following data will be

(a) f(2)
(b) 3
(c) 5
(d) 2² + 1

Evaluate ∆(log ax).

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

Find the missing entries from the following

Using Newton’s forward interpolation formula find the cubic polynomial.

Use Lagrange’s formula and estimate from the following data the number of workers getting income not exceeding Rs. 26 per month

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

If u₀ = 560, u₁ = 556, u₂ = 520, u₄ = 385, show that u₃ = 465

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

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

Estimate the production for 1964 and 1966 from the following data

From the following table find the number of students who obtained marks less than 45.

Using Lagrange’s interpolation formula find y(10) from the following table: