Behaviour a function when input is small If I have the function:
$P(N)=\frac{P_0N^2}{A^2+N^2}$, with $P_0, A$ positive constants
For small $N$, am I right in thinking that because $A$ dominates $N$ we have that 
$P(N) \approx \frac{P_0N^2}{A^2}$

More precisely, we can write for $A^2>N^2$
$$\begin{align}
P(N)&=P_0\left(\frac{N^2}{A^2+N^2}\right)\\\\
&=P_0\left(\frac{(N/A)^2}{1+(N/A)^2}\right)\\\\
&=P_0\frac{N^2}{A^2}\sum_{k=0}^\infty (-1)^k\left(\frac{N^2}{A^2}\right)^{k}\\\\
&=\frac{P_0N^2}{A^2}-P_0\frac{N^4}{A^4}+P_0\frac{N^6}{A^6}+O\left(\frac{N^8}{A^8}\right)
\end{align}$$
Therefore, if we retain only the first term in the expansion we can formally write
$$P(N)\approx \frac{P_0N^2}{A^2}$$
where the approximation error is of order $(N/A)^4$.
