For the following questions answer them individually
A root $$\alpha$$ of equation f(x) = 0 can be computed to any degree of accuracyif a ‘good’ initial approximation $$ X_0 $$ is chosen for which
The shift operator E is defined as
$$ E [f(X_i)] = f (X_i + h) $$ and $$ E^{-1} [f(X_i)] = f (X_i - h) $$
Then $$ \triangle $$ (forward difference) in terms of E is
The formula $$ \int_{x0}^{xn} y(n) dx \simeq h/2 (y_0 + 2y_1 + ..... + 2y_{n - 1} + y_n) -h/12 ( \triangledown y_n - \triangle y_0) -h/24 (\triangledown^2 y_n + \triangle^2 y_0) -19h/720 (\triangledown^3 y_n - \triangle^3 y_0) $$ ....... is called
The cubic polynomial y(x) which takes the following values: y(0) = 1, y(1) = 0, y(2) = 1 and y(3) = 10 is,