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)

∇ ≡ _______.

(a)

1+E

(b)

1 - E

(c)

1− E⁻¹

(d)

1+ E⁻¹

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