Your basic idea is correct: you have to find the limit of f(n)/g(n) as n grows without bound. Unfortunately there is no easy way to compute the exact limit in PHP, since that requires symbolic computations which is best left to a computer algebra system such as Mathematica or Maxima.
You can approximate the limit by computing f(n)/g(n) for increasing values of n and seeing if you get a sequence that approaches a fixed value. For example:
$n=1;
while ($n < 1e300) {
$A = f($n)/g($n);
echo $A, "\n";
$n *= 1e12;
}
In this particular case the sequence of f(n)/g(n) seems to grow without bound, so the numerical evidence suggests that f(n) is in Ω(g(n)). This is not a proof though; symbolic methods are needed for that.