Undefined Limits as k--> 0 1. The problem statement, all variables and given/known data lim(k-->0) [ (-mg)/k + v*e^(kt/m) + (mg)/k*e^(kt/m)] ,the end result of this limit is ultimately supposed to be v -gt (or the velocity of an object at any time t neglecting air resistance). 2. Relevant equations This equation comes from the differential equation dv/dt - k/m *v =g ,then using integrating factors (the equation itself is a linear ODE) I found: v = (-mg)/k + ce^(kt/m) ,where c is found by solving for the initial condition v(0)=v0 where v0 = (-mg)/k + c(1) --> c = v0 + mg/k 3. The attempt at a solution I've spent literally a few hours pouring over this, frustrated as hell that I couldn't solve a simple limit!! I tried first taking the natural log of the whole thing, then I tried using all of the rules of exponents separating the e^(x)s. Then I tried working with the differential equation for a while but ultimately was never able to find a way to fully end up with a defined answer - ie. I was unable to completely eliminate x^(-1) or ln(x) prior to taking the limit as x-->0.