Q6Mathematics II

Question

Q.6. Show that the field defined by $a = (x^{2} + x y^{2}) i + (y^{2} + x^{2} y) j$ is irrotational.

Answer 1

In mathematical analysis, a power series in one variable $x$ is explicitly an infinite series of the exact form:

f (x) = n = 0 \sum \infty c_{n} (x - a)^{n} = c_{0} + c_{1} (x - a) + c_{2} (x - a)^{2} + c_{3} (x - a)^{3} + \dots

$a$ = The specific center of the power series.
$c_{n}$ = The constant coefficients of the series.
$x$ = The independent variable.

This series mathematically absolutely converges (yields a finite value) for specific values of $x$ strictly falling within an interval centered entirely around $a$ , known as the Radius of Convergence.

Q6Mathematics II

Question

Answer