I have a BA in Mathematics. The limit is indeed determined by the direction you approach the limiting value.
When given without specification, the limit is implied to come from the left, meaning it increases towards the limiting value, which is why you see +inf.
This is just not true. The normal limit we have here means a limit would have to exist from both directions and they should be equal. They’re not, so the limit doesn’t exist.
One-sided limits would be denoted by x -> 5– and x -> 5+ or similar.
PS: in complex analysis, there is no distinction between +infty and -infty, so there it would be correct to say the function has limit infty at 5.
You’re right. But in this case, which is the case I was referring to, there is no two sided limit. It is discontinuous. It is in this case which I was referring to. Sorry for not being clear.
In my experience with maths, there’s a whole bunch of different conventions all over the place, so it might’ve genuinely been how they were taught, even if you were taught differently…
I have a BA in Mathematics. The limit is indeed determined by the direction you approach the limiting value.
When given without specification, the limit is implied to come from the left, meaning it increases towards the limiting value, which is why you see +inf.
This is just not true. The normal limit we have here means a limit would have to exist from both directions and they should be equal. They’re not, so the limit doesn’t exist.
One-sided limits would be denoted by x -> 5– and x -> 5+ or similar.
PS: in complex analysis, there is no distinction between +infty and -infty, so there it would be correct to say the function has limit infty at 5.
You’re right. But in this case, which is the case I was referring to, there is no two sided limit. It is discontinuous. It is in this case which I was referring to. Sorry for not being clear.
In my experience with maths, there’s a whole bunch of different conventions all over the place, so it might’ve genuinely been how they were taught, even if you were taught differently…
Yeah, that’s my experience too. When we did this in school we always defined from which side we were approaching the function.
Yeah but then it should be negative infinite, cause if x<8 the fraction is negative.
Ah, I misread the - as a +. You’re correct! Sorry, I just woke up and am in the middle of my morning doomscrolling sesh
Conveniently modeled with the same limit.
Though I’m not sure what negative doom is and what happens when it approaches infinity.