Find the missing term from the following data.

x	20	30	40
y	51	-	34

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

Find the missing term from the following data

x	1	2	3	4
f(x)	100	-	126	157

When h = 1, find Δ (x³).

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

Find \(\Delta e^{x}\)

Find \(\Delta^{2} e^{x x}\)

Find \(\Delta \log (a x) .\)

Evaluate \(\Delta\left(\frac{1}{x}\right)\) y taking 1 as the interval of differencing.

Prove that \(f(3)=f(2)+\Delta I(1)+\Delta^{2} f(1)\) by taking 1 will givea- as the interval of differencing. 

Calculate a forward difference table for the following data

x	20	30	40	50
y	51	43	34	24

 

Construct a forward difference table for \(\mathrm{y}=\mathrm{f}(x)=x^{2}+2 x+2 \text { for } x=1,2,3,4\)

Construct a forward difference table for the following data f(0) = 1, f(1) = 3, f(3) = 55.

Show that \(\Delta=\mathrm{E}-1\)

Write the relationship between 
(i) \(\Delta \) and E
(ii) \(\nabla \text { and } E\)