On adding terms to limits Is it always possible to add terms into limits, like in the following example? (Or must certain conditions be fulfilled first, such as for example the numerator by itself must converge etc)
$\lim_{h \to 0} {f(x)} = \lim_{h \to 0} \frac{e^xf(x)}{e^x}$

It's not clear to me what "add terms into limits" is supposed to mean in general.  In your example, you're not really doing anything: $f(x)$ and $\dfrac{e^x f(x)}{e^x}$ are equal, so any well-defined operation on them produces the same results. 
