Terminal velocity and drag force in one dimention

[Lucien1011]

In one dimensional cases, will the velocity of a particle tend to the terminal velocity unregardless of any combinations of forces?
I try to investigate this equation: mv^'+bv=F(t)
Using the mathematics theorem at the botton, I found that v --> F(c)/m as t tends to infinity. (where c is some constant)

[Thm: if w(x) and u(x) are continuous functions and u(x)>=0, then for a<=x<=b, then {w(x)u(x)}:b,a=w(c)*{u(x)}:b,a for some c lies between a and b]
the notation {f(x)}:b,a represents the definite integral from a to b with repect to x. Sorry for the unusual notation, as I don't know how to type the integral.

Sorry for the poor presentation too. I intended to write the result on a piece of paper and scan it into the computer but my scanner is out of order now.

 

[matematikawan]

Looks fine to me if the theorem is correct. How are you going to determine the value of c?

 

[Lucien1011]

Looks fine to me if the theorem is correct. How are you going to determine the value of c?

Oh yeah. I neglect that the upper and lower limit in the thm should be constants.