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Current time:0:00Total duration:2:17

Video transcript

all right we have a graph of y is equal to f of X and we want to figure out what is the limit of f of X as X approaches negative 3 and if we just look at x equals negative 3 it's really hard to see at least based on how this graph looks how what f of negative 3 is and if anything it looks like we has we have an asymptotic discontinuity here it looks like on the left side of x equals negative 3 it looks like we're approaching I guess you could say infinity and on the right side what it looks like we're approaching infinity as well and we could just look at that we could say well look what is f of negative 5 that's 4 f of negative 4 is looks like it's around around 8 F of negative 3 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 3 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 3 from the left-hand side let's think about what's as we approach negative 3 from the right-hand side so this is F of negative 1 F of negative 2 F of negative 2 point 5 looks like it's up here someplace X F of negative 2 point 9 would be even higher F of negative two point nine nine nine it looks like it would just once again approach infinity so this type of limit in some context you would say that this limit doesn't exist doesn't doesn't exist in the formal sense so that's one way to think about it and some in some context you will people you will hear people say that this limit since from the left and from the right it looks like it's going to infinity sometimes you will see people say that it is approaching infinity and so this is depending on what type of a class what type of a context you're in but it is a traditional sense of the limit or in the technical sense there there are ways that you can define limits where this would make a little bit more sense but in the moment in the traditional definition of a limit it would be you would say that this limit does not exist