It's a domain specific answer, even ignoring the 0/0 case.
And also even ignoring the "which side of the limit are you coming from?" where "a" and/or "b" might be negative. (Is it positive infinity or negative infinity? The sign of "a" alone doesn't tell you the answer)
Because sometimes the question is like "how many things per box if there's N boxes"? Your answer isn't infinity, it's an invalid answer altogether.
The limit of 1/x or -1/x might be infinity (or negative infinity), and in some cases that might be what you want. But sometimes it's not.
Sometimes yes, sometimes no?
It's a domain specific answer, even ignoring the 0/0 case.
And also even ignoring the "which side of the limit are you coming from?" where "a" and/or "b" might be negative. (Is it positive infinity or negative infinity? The sign of "a" alone doesn't tell you the answer)
Because sometimes the question is like "how many things per box if there's N boxes"? Your answer isn't infinity, it's an invalid answer altogether.
The limit of 1/x or -1/x might be infinity (or negative infinity), and in some cases that might be what you want. But sometimes it's not.