If an object of mass $m$ is dropped from rest, one model for its speed $v$ after $t$ seconds, taking air resistance into account is:

$v=\dfrac{mg}{c} \left(1-e^{(-c t / m)}\right)$

Where $g$ is the acceleration due to gravity and $c$ is a positive constant. (In chapter 9 we will be able to deduce this equation from the assumption that the air resistance is proportional to the speed of the object.

(a) Calculate $\lim\limits_{t\rightarrow \infty} v$. Your answer may depend on $c$, $g$, and $m$.

(b) For fixed $t$, use L'Hospital's rule to calculate $\lim\limits_{m\rightarrow \infty} v$. Your answer may depend on $c$, $g$, and $t$.