Question

Find lim (with x¨‡ under it) (x^2-1)/x or state that the limit does not exist.

I'm so lost with what to do with limits...I tried to simplify the expression to lim x+lim -1/x, but from there I'm pretty dumbfounded.
If anybody could help me out I'd really appreciate it.

Answer 1

I guess symbols do not post, but it is just lim with (x->infinity) underneath

Answer 2

You are looking for the limit of

x^2 -1
-------
x

as x ---> oo

well when x is very large the numerator is x^2 and the one does not amount to a hill of beans so what you really have is

x^2
---
x

which is of course x
which goes to infinity as x goes to infinity