(a) Using Newton's interpolation formula, compute the value of $\sqrt…

Question

(a) Using Newton's interpolation formula, compute the value of $\sqrt{15.5}$, given that $\sqrt{5} = 2.236$, $\sqrt{10} = 3.162$, $\sqrt{15} = 3.872$, $\sqrt{20} = 4.472$, $\sqrt{25} = 5$.

(b) Using Newton's divided difference formula, construct a polynomial which takes the following values:

$x$: 3, 7, 9, 10

$f(x)$: 168, 120, 72, 63

Hence or otherwise evaluate $f(6)$.

(c) Evaluate $\int_{0}^{1} \sqrt{1 - x^2} dx$ by Trapezoidal and Simpson's $1/3$ rule taking $h = 0.1$.