If an object of mass [math] is dropped from rest, one model for its speed [math] after [math] seconds, taking air resistance into account is:

[math]

Where [math] is the acceleration due to gravity and [math] 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 [math]. Your answer may depend on [math], [math], and [math].

(b) For fixed [math], use L'Hospital's rule to calculate [math]. Your answer may depend on [math], [math], and [math].