# Calculate the limit of a falling object (with air-resistance) using L'Hopital's rule.

This problem has been particularly confusing to me:

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

v=[(mg)/(c)][1-e^([-ct]/m)]

where g is the acceleration due to gravity and c is a positive constant.

(a)Calculate the limit as t approaches infinity of v. What's the meaning of this limit?

(b)For fixed t, use L'Hospital's rule to calculate the limit as m approaches infinity of v. What can you conclude about the speed of a very heavy falling object?"

https://brainmass.com/math/calculus-and-analysis/limit-falling-object-using-hopitals-rule-36462

#### Solution Preview

(a)

v=[(mg)/(c)][1-e^([-ct]/m)]

when t approaches to infinity, v=mg/c. This velocity is called terminal velocity which means when air resistance is considered, the ...

#### Solution Summary

The limit of a falling object (with air-resistance) is calculated using L'Hopital's rule.