Limits from graphs: asymptote

Video udskrift

- [Voiceover] Alright we have a graph of y is equal to f of x and we wanna figure out what is the limit of f of x as x approaches negative three. And if we just look at x equals negative three, it's really hard to see at least based on how this graph looks, how what f of negative three is and if anything, it looks like we have an asymptotic discontinuity here. It looks like on the left side of x equals negative three, it looks like we are approaching, I guess you can say infinity and on the right side, it looks like we are approaching infinity as well. And we can just look at that and say, What is f of negative 5? That's four. F of negative four is looks like it is around, I don't know around eight. F of negative three is off the charts. F of negative, if we continued with this trend and if we were to asymptote towards this line right over here, this vertical asymptote, it looks like as we get closer and closer to negative three that the value of the function at that point is approaching, is getting closer and closer to infinity, at least that's what it looks like from what we can see on this graph as we approach negative three from the left hand side. Let's think about as we approach negative three from the right hand side, so this is f of negative one, f of negative two, f of negative 2.5 looks like it's up here some place, f of negative 2.9 would be even higher, f of negative 2.999 looks like it will just once again approach infinity so this type of limit in some context you'd say this limit doesn't exist doesn't doesn't exist in the formal sense so that's one way to think about it. In some contexts, you'll hear people say that this limit since from the left and from the right, it looks like it's going to infinity. Sometimes you'll see people say that it's approaching infinity and so this is depending on what type of a class what type of a context you're in but in the traditional sense of the limit or in the technical sense, there are ways that you can define limits where this will make a little bit more sense but the traditional definition of a limit, it would be, you would say that this limit does not exist.