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Connecting limits at infinity notation and graph

Sal analyzes a function with an asymptote and finds the correct description of the two one-sided limits of the function at that asymptote.

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  • starky sapling style avatar for user Sujay Saundatti
    Do limits have a application without calculus?
    (2 votes)
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  • duskpin ultimate style avatar for user vikawb02
    How do we know if we should approach from the left or the right side? I started doing this problem by myself first and when I see x-->6+ I automatically went for left tor right because it seemed to me that I was going from minus infinity to +6...
    (2 votes)
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    • leaf green style avatar for user kubleeka
      6⁺ means the limit from the right, because we're looking at the region in the positive direction (to the right) of 6. 6⁻ is from the left because we're looking at the region in the negative direction (to the left).
      (3 votes)
  • blobby green style avatar for user Aztec Binaynay
    I'm looking for ways one can solve a limit function through different methods, and found that my school and Khanacadamy's way of tackling these materials are somewhat different. I'm not sure if Sal mentioned this (my calculus book discussed this btw) but you could also find algebraically the limit of a function as x approaches infinity by dividing by the highest power of a variable. did sal mention this somewhere?
    (1 vote)
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  • leafers seedling style avatar for user Pikmaniac
    In this video: https://www.khanacademy.org/math/differential-calculus/dc-limits/dc-limits-from-graphs/v/one-sided-limits-from-graphs-asymptote
    it was said that a limit that approaches infinity "does not exist".
    (Maybe because of the epsilon-delta defintion)

    Now we say that negative Infinity and positive infinity or just infinity is a valid answer. What should I write in a test? I prefer to write infinity but this goes against the epsilon-delta defintion.
    (0 votes)
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Video transcript

- [Voiceover] We're asked to select the correct description. It looks like all the descriptions deal with what is the limit of f of x as we approach six from either the right hand side or from the left hand side, so let's think about that. So first let me just do the left hand side. So the limit of f of x as we approach six from the left hand side, what is this going to be equal to? So as we approach from the left hand side we can see f of four is a little under two, f of five looks like it's around three, f of 5.5 looks like it's a lot higher, f of 5.75 even is just going off the charts, so it looks like this is going unbounded in the positive direction, so we could say that this right over here is positive infinity, and if we were to think about the limit of f of x as we approach six from the right side, what is this going to be? Well here, f of seven, it's negative, f of 7.5 is even more negative, f of 6.5 is even more negative, f of 6.1 is way more negative than that, f of 6.01 would be even more negative than that. So it looks like this is unbounded in the negative direction, so this is negative infinity. so let's see which of our choices match up to that. so the way they listed it, they listed the limit from the right direction first, so that's this one, so the limit of f of x as x approaches six from values greater than six, we have negative infinity, so that is these two choices, these two choices say that, so we're gonna rule out those two choices. And then we think about as we approach six from the left hand side, we see that we go to positive infinity, and that is this choice right over here, so we rule out that one, and that is what we will pick.