Say if I have some expression $\frac{h}{k^2}$ or $\frac{h^2}{k}$ and I send both $h,k \rightarrow 0$. Can I say that the expressions tend to zero without further explanation?
When we send these constants to zero are we sending them to zero at the same speed? Or even assuming similar initial conditions? E.g if in the first expression we were to assume that $k^2 < h \implies \frac{1}{k^2} > \frac{1}{h}$ and hence $$\frac{h}{k^2}>\frac{h}{h}=1$$
This leads me to believe that we must provide a further explanation. i.e that the restriction $k^2 > h$ must hold in order for $\frac{h}{k^2}\rightarrow 0$
Am I thinking about this correctly or am I looking at this the wrong way?