What does asymptotic behavior mean? I am asked to find that but I'm not sure what they are looking for. How do you write one?

Question

anonymous · Answer

For example, what would be the asymptotic behavior of $$\frac{ x }{ x^2-x-2 }$$?

phi · Answer

when x = -1  the bottom becomes  -1*-1  - (-1) -2 = 1 + 1 -2 = 2-2=0
dividing by 0 is not allowed...
however if let x get very close to -1, the bottom gets very close to 0 (it is a very tiny number)

when you divide by a tiny number you get a big number.  Example:  1/ 0.001 = 1000
(use a calculator if you don't see this)
as the bottom gets closer to 0 (gets tinier) you divide by a tinier number and get a bigger number.  the numbers get bigger as x gets closer to -1, and zoom up to infinity

you never get to x =-1 but you asymptote to x=-1

anonymous · Answer

hmmm I get what you are saying, but is there a specific way to write asymptotic behavior?

anonymous · Answer

yes 
$$\lim_{x\to \infty }\frac{ x }{ x^2-x-2 }=0$$