Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-L] My 2 cents re: irresistible forces and immovable objects.

Following up on Bob Sciamanda's nifty post on 01/30/2018 11:47 AM...

The mathematical limit does not have to be well-behaved
or even well-defined. The limit might simply not exist.

Explicit example:

F = t^2
which is clearly irresistible in the limit as t → ∞

m = t [1-sin(t)] + t^3 [1+sin(t)]
which oscillates between 2t and 2t^3 but is in any
case immovable in the limit as t → ∞.

The ratio F/m exists for any finite t, but does not
exist in the limit. The sequence does not converge.

Hint: draw the graph.
Or apply l'Hôpital's rule a few times.