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## Calculus, all content (2017 edition)

### Unit 1: Lesson 19

Unbounded limits (vertical asymptotes)- Infinite limits intro
- Connecting limits at infinity notation and graph
- Infinite limits: graphical
- Analyzing unbounded limits: rational function
- Analyzing unbounded limits: mixed function
- Infinite limits: algebraic
- Visually determining vertical asymptotes (old)

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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.

## Want to join the conversation?

- Do limits have a application without calculus?(2 votes)
- 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)
- 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)

- 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)
- why i dont know but whenever is ee such graphs i try to calculate the formula of the equation. wouldnt it be good to express them also?(1 vote)

- 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".1:28

(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)

## 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.