I have the following question:
Given,
$f_1(a), f_2(a),\ldots, f_n(a)$ and $g_1(a), g_2(a),\ldots, g_n(a)$ are strictly increasing positive "polynomial" functions of $a$.
It is also known that
$\frac{f_1(a)}{g_1(a)}, \frac{f_2(a)}{g_2(a)},\ldots,\frac{f_n(a)}{g_n(a)}$ are strictly increasing functions of $a$.
Does
\begin{equation} \frac{f_1(a)+f_2(a)+\cdots+f_n(a)}{g_1(a)+g_2(a)+\cdots+g_n(a)} \end{equation}
EVENTUALLY increases with $a$?