Is $g(z + \Delta z).g(z) = g(z)^2$ ?
The full expression is a $\lim_{\Delta z \to 0} \frac {A}{G} $, where $G$ is the left-hand side of the above expression.
It's a question about a solution to a problem that I'm going through, and I can't post it because I don't have enough reps. But the gist of it is that the above expression is taken to be true and thus he factors a $g(z)^2$ out of the limits in the denominator.
I'd appreciate it if somebody explains how this is possible. Thanks!