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  • - [Voiceover] Over here we have the graph of

  • y is equal to g of x.

  • What I wanna do is I wanna figure out

  • the limit of g of x

  • as x approaches positive six

  • from values that are less than positive six

  • or you could say from the left, from the, you could 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 take different x-values that approach six

  • from the left and look at what the values

  • of the function are.

  • So g of two, looks like it's a little bit more than one.

  • G of three, it's a little bit more than that.

  • G of four, looks like it's a little under two.

  • G of five, it looks like it's around three.

  • G of 5.5, looks like it's around five.

  • G of, let's say 5.75,

  • looks like it's like nine.

  • And so, as x gets closer and closer to six

  • from the left, it looks like the value of our function

  • becomes 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, we're not talking

  • about a specific number.

  • 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.

  • Now 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 six from the right-hand side,

  • well, let's see.

  • We have g of eight is there, go of seven is there,

  • g of 6.5, looks like it's

  • a little less than negative three.

  • G of 6.01, little even closer to negative three.

  • G of 6.0000001 is very close to negative three.

  • So it looks like this limit right over here,

  • at least looking at it graphically,

  • it looks like when we approach six

  • from the right, looks like the function

  • is approaching negative three.

  • But from the left, it's just unbounded,

  • so we'll say it doesn't exist.

- [Voiceover] Over here we have the graph of

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A2 初級 美國腔

圖的單邊限制:漸近線(One-sided limits from graphs: asymptote | Limits and continuity | AP Calculus AB | Khan Academy)

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    yukang920108 發佈於 2022 年 06 月 30 日
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