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Main content
Current time:0:00Total duration:2:27
AP.CALC:
LIM‑1 (EU)
,
LIM‑1.C (LO)
,
LIM‑1.C.1 (EK)
,
LIM‑1.C.2 (EK)
,
LIM‑1.C.3 (EK)
,
LIM‑1.C.4 (EK)

Video transcript

so over here we have the graph of y is equal to G of X and what I want to do is I want to figure out the limit of G of X as X approaches positive 6 from values that are less than positive 6 or you could say from the left from the you say the negative direction so what is this going to be equal to and if you have a sense of it pause the video and give a go at it well to think about this let's just a pro let's just take different X values that approach 6 from the left and look at what the values of the function are so G of 2 looks like it's a little bit more than 1 G of 3 it's a little bit more than that G of 4 looks like it's a little under 2 G of 5 it looks like it's around 3 G of 5.5 looks like it's around 5 gia let's say five point seven five looks like it's like nine and so as X gets closer and closer to 6 from the left it looks like the value of our function just gets comes unbounded it's just getting infinitely large and so in some context you might see someone write that maybe this is equal to infinity but infinity isn't it we're not talking about a specific number and if we're if we're talking technically about limits the way that we've looked at it what is you'll sometimes see this in some classes but in this context especially on the exercises on Khan Academy we'll say that this does not exist not exist this thing right over here is unbounded and this is interesting because the left handed limit here doesn't exist but the right handed limit does if I were to say the limit of G of X as X approaches 6 from the right hand side well let's see we have G of 8 is there G of 7 is there G of 6.5 looks like it's a little less than negative 3 G of 6.0 one little even closer to negative 3 G of 6 point zero zero zero zero zero zero one it's very close to Nega of three so it looks like this limit right over here at least looking at it graphically it looks like when we approach 6 from the right looks like the function is approaching negative 3 but from the left it's just unbounded so we'll say it doesn't exist
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