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**Undefined Limits as k--> 0**

## Homework Statement

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).

## Homework 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

## 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.