Limits describe how a function behavesnear a point, instead of at that point. This simple yet powerful idea is the basis of all of calculus.

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boddhulas

7 years agoPosted 7 years ago. Direct link to boddhulas's post “In the last question, how...”

In the last question, how does

x→7

lim

g(x)

exist? It has two locations right?•

(135 votes)

Rachel

7 years agoPosted 7 years ago. Direct link to Rachel's post “The limit exists because ...”

The limit exists because the same y-value is approached from both sides. It does not have two locations because the open circle is a just gap in the graph. The closed circle is the actual y-value for when x=7.

(305 votes)

K M

7 years agoPosted 7 years ago. Direct link to K M's post “In problem 5 why can one ...”

In problem 5 why can one of the answers be x→6? but not x→3?

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(19 votes)

Dave

5 years agoPosted 5 years ago. Direct link to Dave's post “I assume you are talking ...”

I assume you are talking about the last example. As you approach x=6 from the left you move closer to 3; AND as you approach x=6 from the right, you also moce closer to 3.

As you move closer to x=3 form the left you move closer to 3, BUT when you move closer to x=3 from the right, you move closer to 6.

They must be moving to the same value of y from both sides if you are not going to specify the side in th limit notation.

Amanda Lu

7 years agoPosted 7 years ago. Direct link to Amanda Lu's post “For the last question, ho...”

For the last question, how is there a limit for x-->6? There is a point there. I thought there could only be limits if there were open dots.

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(11 votes)

Stephen.Burke

7 years agoPosted 7 years ago. Direct link to Stephen.Burke's post “As Sal explained both in ...”

As Sal explained both in the video Limits intro, and in the text, the beauty of limits, and one property of limits, is that they do not explain the actual point of the graph, but the behavior leading up to that point. Whether there is a point at f(x)= 6 or a hole, that would not change that there still is a limit, unless a jump occurs between the two leading lines.

(43 votes)

sam

a year agoPosted a year ago. Direct link to sam's post “learning this calculus co...”

learning this calculus concept here was actually super fun. although i know this will take many hours, the hours will be exhilarating! i'm going to try and conquer calculus in 2 weeks. (today is june 24th, i have until july 10th)

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(23 votes)

Master Mind

a year agoPosted a year ago. Direct link to Master Mind's post “How is calc going so far ...”

How is calc going so far for ya'll

(2 votes)

1249424990bsq

5 years agoPosted 5 years ago. Direct link to 1249424990bsq's post “what is the difference be...”

what is the difference between APcalculus AB and APcalculus BC?

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(7 votes)

Alex

5 years agoPosted 5 years ago. Direct link to Alex's post “More specific course cont...”

More specific course content is given on the College Board website.

Essentially, AB is equivalent to Calc 1, while BC is equivalent to Calc 1 and 2. AB covers limits, derivatives, and integrals. BC covers everything that AB does, in addition to derivatives of vector-valued functions, polar functions, parametric functions, planar motion, Euler's Method, improper integrals, integration by parts, arc length, polar areas, the logistic model, and (a whole unit on) series. Hope that I helped.

(22 votes)

cr7neymar9

a year agoPosted a year ago. Direct link to cr7neymar9's post “over a year ago is was on...”

over a year ago is was on algebra 1 videos now I'm on calculus finally. lets goo

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(17 votes)

mezomaxim516

a year agoPosted a year ago. Direct link to mezomaxim516's post “Bro what? Congratulations...”

Bro what? Congratulations, but be sure you have all the fundamentals down from Algebra 1 and 2 along with Geometry and precal. You don't want to jump ahead into something that you don't understand. Be sure to have strong foundations before continuing.

(0 votes)

mzhang

7 years agoPosted 7 years ago. Direct link to mzhang's post “the plot has open dots an...”

the plot has open dots and closed dots. what does that symbolize in limits?

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(5 votes)

Allam Amzad

7 years agoPosted 7 years ago. Direct link to Allam Amzad's post “Open dots means it doesn'...”

Open dots means it doesn't include that point and closed dots mean it does include that point. For example, a open dot at 6 means it can't be 6 but it can be 5.999999 or 6.000001, just not 6. A closed circle for the point 6 would mean it includes 6.

(21 votes)

Aiden Houser

a year agoPosted a year ago. Direct link to Aiden Houser's post “On problem 5, there are l...”

On problem 5, there are limits even though the function is not undefined right? For example, as x approaches 6

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(5 votes)

Venkata

a year agoPosted a year ago. Direct link to Venkata's post “Correct. If a function is...”

Correct. If a function is defined at a point, there can be two cases:

1. It is defined but not continuous (like at x = 7)

2. It is defined and continuous (like at x = 6)

Note that even though the function is continuous and the limit exists at x = 6, it is not

**differentiable**, a term you'll learn later on. Revisit this answer once you learn differentiability. You'll see what I mean(12 votes)

curiousfermions

5 years agoPosted 5 years ago. Direct link to curiousfermions's post “When we take a limit, we ...”

When we take a limit, we approach a specific x value from both sides. But there is

*an infinite number of numbers between any two numbers*. So when we are approaching x,**can****we****ever****really****get****there**? And if we can not, then does the calculus give us an answer with really really really really really small flaw that does not create problem in any calculation? Or is it 100% flawless?•

(7 votes)

Moon Bears

5 years agoPosted 5 years ago. Direct link to Moon Bears's post “This is the issue that a ...”

This is the issue that a lot of people had in the development of the calculus. The solution was quite clever, the idea is that you can get "arbitrarily close" that is given any epsilon positive there's a delta such that |x-a| < delta implies |f(x) - f(a)| < epsilon. If this is true FOR EVERY epsilon, then we say the limit exists and the function is continuous. Is it 100% flawless? Not really, but the thing is it's useful. Using these ideas we were able to build up a foundation for calculus which eventually lead to the physics that put man on the moon. The point is it gets results.

(5 votes)

Manaf01

a year agoPosted a year ago. Direct link to Manaf01's post “first day learning calcul...”

first day learning calculus

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(10 votes)