Question

limit as x approaches 3 of (x+5)/(x^2-9)

Answer 1

\[\lim_{x \rightarrow 3}\frac{ x+5 }{ x^2-9}\]

Answer 2

\[\lim_{x \rightarrow 3}\frac{ x+5 }{(x+3)(x-3)}\]

Answer 3

is there anything else I can do, other than to state that x=3 is a vertical asymptote and therefore the limit does not exist

Answer 4

We can be a little bit more accurate about it I guess.
If the left and right sided limits do not agree, then the limit does not exist.
That's what is happening here.

It's approaching negative infinity from one side,
and positive infinity from the other side.

Answer 5

yes you are correct, I should write those limits statements concerning the right hand limit and left hand limit.....

Answer 6

\[\Large\rm \lim_{x\to3^-}\frac{x+5}{(x+3)(x-3)}=\frac{3^-+5}{(3^-+3)(3^--3)}=\frac{+}{(+)(-)}\]Just keep track of the signs or something..
That's what I like to do at least :d

So this left sided limit would be approaching negative infinity it looks like.

Answer 7

yes, I was probably going to use the graph or a sketch of the graph.....thanks

Answer 8

ah c: