Δ²y₀ = _______.

(a)

y₂ −2y₁ + y₀

(b)

y₂ + 2y₁ − y₀

(c)

y₂ + 2y₁ + y₀

(d)

y₂ + y₁ + 2y₀

E ≡ _______.

(a)

1 + Δ

(b)

1 - Δ

(c)

1 + ∇

(d)

1 - ∇

If c is a constant then Δc = _______.

(a)

c

(b)

Δ

(c)

Δ²

(d)

0

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

(a)

f(2x)

(b)

f(x+ h)

(c)

f (x)

(d)

Δf(x)

For the given points (x₀, y₀) and (x₁, y₁) the Lagrange’s formula is _______.

(a)

\(y(x)=\frac{x-x_{1}}{x_{0}-x_{1}} y_{0}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{1}\)

(b)

\(y(x)=\frac{x_{1}-x}{x_{0}-x_{1}} y_{0}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{1}\)

(c)

\(y(x)=\frac{x-x_{1}}{x_{0}-x_{1}} y_{1}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{0}\)

(d)

\(y(x)=\frac{x_{1}-x}{x_{0}-x_{1}} y_{1}+\frac{x-x_{0}}{x_{1}-x_{0}} y_{0}\)

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)

∆f(x + 3h) ______________

(a)

f(x + 3h) - f(x + 4h)

(b)

f(x + 4h) - f(x + 3h)

(c)

f(x + h) - f(x)

(d)

f(x + 2h) - f(x + 3h)

If c is a constant, then Δc = ______________

(a)

c.∆

(b)

c.∇

(c)

0

(d)

1

Let y = f(x) be a given function of x and y₀, _y1., yn be the values of y at x = x₀, x₁, x₂ ... respectively, then ∇y₁ is ______________

(a)

y₁ - y₂

(b)

y₀ - y₂

(c)

y₀ - y₁

(d)

y₁ - y₀