Limit function and DirectedInfinity as output: Interpretation

Question

I tried to compute the following limit:

In[12]:= Limit[-A/2 x - 2 x, x -> +Infinity]

Out[12]= DirectedInfinity[-2 - A/2]

Does the output tell me that the software cannot evaluate the sign because it does not know the sign of A? And does it tell me that the solution is for sure plus or minus infinity?

Thank you in advance.

Answer 1

Does the output tell me that the software cannot evaluate the sign because it does not know the sign of A?

In a way, yes. But it does not even assume A to be real. What if A==I?

And does it tell me that the solution is for sure plus or minus infinity?

In a way, yes. But this is not generally correct. If A==4, then the answer is zero.

BTW newer versions give the answer as

(-2 - A/2) ∞

Also, in newer versions of Limit can do this:

Limit[-A/2 x - 2 x, x -> +Infinity, GenerateConditions -> True]

(* ConditionalExpression[(-2 - A/2) ∞, A != -4] *)

Finally, note that Infinity is also just DirectedInfinity in disguise.

Infinity//FullForm
(* DirectedInfinity[1] *)

-Infinity//FullForm
(* DirectedInfinity[-1] *)