Consider the data of $f(x)$ given in the table.

$i$	$0$	$1$	$2$
$x_i$	$1$	$2$	$3$
$f(x_i)$	$0$	$0.3010$	$0.4771$

The value of $f(1.5)$ estimated using second-order Newton’s interpolation formula is ________________ (rounded off to 2 decimal places).

Consider the following recursive iteration scheme for different values of variable P with the initial guess x₁ = 1:

$${x_{n + 1}} = {1 \over 2}\left( {{x_n} + {P \over {{x_n}}}} \right)$$, n = 1, 2, 3, 4, 5

For P = 2, x₅ is obtained to be 1.414, rounded-off to three decimal places. For P = 3, x₅ is obtained to be 1.732, rounded-off to three decimal places. If P = 10, the numerical value of x₅ is __________. (round off to three decimal places)

The quadratic approximation of $$f\left( x \right) = {x^3} - 3{x^2} - 5\,\,$$ at the point $$x=0$$ is

The estimate of $$\int\limits_{0.5}^{1.5} {{{dx} \over x}} \,\,$$ obtained using Simpson's rule with three-point function evaluation exceeds the exact value by