# A Limits Question

This question involves a graph, but, unfortunately, I have no means of reproducing it. I shall try my utmost to describe it, or rather the section of it that confounds me.

Consider the function f. For what values of x_0 does the lim x-->x_0 f(x) exist, where -9<= x_0 <=4?

The answer says that at the value x_0 = -6 the limit does not exist (d.n.e.), but I think the limit is positive infinity and don't know why it d.n.e.

Here is the description:

f(-6) = 3, so there is a black point at (-6,3). Now as x approaches -6 from the left side, the curve goes upward, or without bound (+infinity). As x approaches -6 from the right side, there is another curve that goes upward, or without bound (+infinity), so it seems like there is a vertical asymptote at x_0 = -6 (but a point exists at -6).

This is the section that baffles me. If you need a clearer description, I shall try to do my best.

Thanks.

LeonhardEuler
Gold Member
To say that a limit is infintiy implies that the limit does not exist. The definition of a limit does not allow infinite limits (although it does allow limits where a variable is allowed to approach infinity).

So D.N.E. implies that the limit is not close to a single real number? I am still confused over the term . . . When is the limit in this case +infinity? Is it because of how the question is worded?? I was trying to follow that two-sided limit of a function rule. . . (Now I feel horribly lost.)