Recent content by Timmo

l'Hopital gets messy indeed. But, hey, at least it's honest. :-p

As x goes to infinity, so does the numerator and the denominator. You get an indeterminate form. So, you might try l'hospital's rule: http://mathworld.wolfram.com/LHospitalsRule.html

Here's a place to start: the particle's position as a function of time in Cartesian co-ordinates is just (1) \stackrel{\rightarrow}{r} =b\stackrel{\rightarrow}{x} + vt\stackrel{\rightarrow}{y} What is the velocity? (2) \frac{d}{dt}\stackrel{\rightarrow}{r} =...

You can't use that equation because that only applies when one has constant acceleration. (1) v= v_0 e^{-t/\tau} (2) x = v_0\int_0^t e^{-\frac{t'}{\tau}} dt' = v_0\tau(1 - e^{-\frac{t}{\tau}}) Solve for time in second equation (2). Then you can substitute that into (1). It will get...

This problem is about damping. You have an object moving against a force proportional to its velocity, but directed opposite to it: F = -bv. The solution is an exponentially decaying one. This is what you got! -2t = ln v + C ===> v = v_0 e^{-2t}

Then I say that this vague definition leads to paradoxes and presents Russell's paradox. How is Russell's paradox supposed to provide a counter-example to Cantor's "definition" of a set? :confused: As Cantor says, a set is a collection of distinct objects. (One can also study multi-sets...