I have the following function $ f(t) = \frac{a(t)}{\sqrt{b(t) + \epsilon(t)}} $ defined for $t\geq 0$. I know that $a(t) > 0$, $b(t) > 0$, $\epsilon(t) \geq 0$ and $\epsilon(t) << b(t) $ $\forall t\geq0$ (and, in particular, $\epsilon(0) = 0$, whereas $b(0)=b_0 >> 0$).
What can I do to find an approximation/expansion for $f(t)$ leveraging on the small size of $\epsilon(t)$? May I use some sort of Taylor/Mac-Laurin expansion? Or some functional-derivative like reasoning?
Thanks in advance