(a) Evaluate $(\Delta + \nabla)^2 (x^2 + x)$. (b) Prove that $\Delta…

Question

(a) Evaluate $(\Delta + \nabla)^2 (x^2 + x)$.

(b) Prove that $\Delta = E\nabla, \nabla = E^{-1}\Delta$.

(c) State Lagrange's interpolation formula and apply it to find $f(7)$ from the following data:

$x$: 5, 6, 9, 11

$f(x)$: 12, 13, 14, 16