Formal definition of limits Part 4: using the definition | AP Calculus AB | Khan Academy

Watch the definition of a limit in action. Created by Sal Khan.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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[elih]

Whenever a point x is within δ units of c, f(x) is within ε units of L

[redorangeyellow]

"let me switch colors just to ease the monotony"

[jony]

Thanks Sal my prof moves so quick I don't understand him at all. You helped me figure out the whole concept.
If you guys don't get it, watch the other two videos he has for background info. They help it all make sense.

[hamdaankhalid]

Sal Khan absolutely love you and the work you do. You helped me from being a high school math failing kid, to someone now majoring in math.

[chanr]

God bless your soul! Jesus, you have no idea how thankful I am. This shit was so confusing when my prof explained it but you made it so easy to understand!

[JORGEMARTINEZMARTIN-xdpe]

As a first-year engineering student who just understood what might be a problem on my next week´s calculus exam, thank you

[rachitaarora]

This video is mind blowing..I don't have words to express what I felt while watching this video. You're so good at explaining things.

[toddcollins]

I was good at math until epsilon delta. Just can't get it and this seems to not help me at all.

[abhayr]

Hey Sal, this is really a lifesaver; I had no idea what this concept was until I saw this video, and now I know exactly what was taught to us for this. BTW, we have this definition only for multivariate calculus, not for single variable calc, for some reason.

[GresaBajraktari]

Your videos are very precious to me. Had many problems in my life during high school so I struggled with maths but the information you provide online helped me to fill my gaps and I am grateful

[avibank]

An entire chapter summarized in 8 minutes. Thanks.

[TheParkourPenguin]

It's 4, because 2 is in the domain of your function and (therefore) you can simply plug in 2 for x in your original function (x^2):
2^2 = 4
Therefore, the answer is 4.

[Kashif_Javaid]

You are right and implicitly implying continuity to prove this limit. Now if you want to show this without continuity and using epsilon/delta definition, how would you do that? a video from Sal would be good!!

[kamalame]

I dont have words to thank you. I was working so hard to learn this but didnt understand anything. Thank you so much for this.

[jdmrchem]

Great! Powerful to learn the fundamentals of proving limits with the epsilon-delta definition.

[ASassyP]

I would fail my calculus class without this channel

[Salma-qyqb]

I have watched every video in this playlist.. EVERY SINGLE ONE OF THE 54 VIDEOS!

[jsmwnyc]

This was an unorthodox solution.
| f(x) - L | < epsilon becomes | 2x - 10 | < epsilon. 2 | x-5 | < epsilon.
| x - c | < delta becomes | x - 5 | < delta.
So, we simplify the epsilon equation by dividing by 2.
| x - 5| < epsilon/2. therefore delta <= epsilon/2. QED.

[Nikifuj]

This may help; obviously there's nothing intuitive here, but just think of ε as being incredibly small and 1/ε as, consequently, being incredibly large. We say that the limit of f(x) as x→w does not exist (or equals complex infinity) if & only if for any ε > 0, there is a δ > 0, such that for all x in the domain of f(x) with |x – w| < δ we have that |f(x)| = 1/ε.

[antikertech]

Very good explanation, thank you sir.
You guys probably should learn calculus from Spivak's book, if you haven't already. For anyone serious with math :)