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Introduction to limits | Limits | Differential Calculus | Khan Academy

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Introduction to limits Watch the next lesson: https://www.khanacademy.org/math/differential-calculus/limits_topic/limits_tutorial/v/limit-by-analyzing-numerical-data?utm_source=YT&utm_medium=Desc&utm_campaign=DifferentialCalculus Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits. About Khan Academy: Khan Academy is a nonprofit with a mission to provide a free, world-class education for anyone, anywhere. We believe learners of all ages should have unlimited access to free educational content they can master at their own pace. We use intelligent software, deep data analytics and intuitive user interfaces to help students and teachers around the world. Our resources cover preschool through early college education, including math, biology, chemistry, physics, economics, finance, history, grammar and more. We offer free personalized SAT test prep in partnership with the test developer, the College Board. Khan Academy has been translated into dozens of languages, and 100 million people use our platform worldwide every year. For more information, visit www.khanacademy.org, join us on Facebook or follow us on Twitter at @khanacademy. And remember, you can learn anything. For free. For everyone. Forever. #YouCanLearnAnything Subscribe to KhanAcademy’s Differential Calculus channel: https://www.youtube.com/channel/UCNLzjGl1HBdZrHXo4Vae3iA?sub_confirmation=1 Subscribe to KhanAcademy: https://www.youtube.com/subscription_center?add_user=khanacademy
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Text Comments (706)
馬善存 (1 day ago)
This guy should seriously be nominated for the Nobel Prize.
GoFuckYourselfYouTube (2 days ago)
For somebody who grew up and has worked in computer science for 30 years, this is confusing as hell. X, Y, Z? So the function of g(x) limit is... What the limit of that function for Y would be... At a certain constraint? I don't get it. Is that what is is? So X is always defined, but in Calculus, the function defines Y? Christ, this is so primitive. Not that I'm saying I'm so smart this is easy- quite the opposite. I feel like it's relearning concepts I should have been taught in the first place! Math is crazy, I will never learn 1% of it.
Noor naser (8 days ago)
zoraiz ahsan (9 days ago)
good job khan G
the direct girl 123 (10 days ago)
at 9:13 he farted i swear 😂
Will Turner (11 days ago)
So here my internet connection has some serious limits. So what'll happen if I approach those limits? Let's say a limit of 5 But as soon as I approach 5 It'll be over Or no,even if I get close to 4 It'll be still be over.
Michael Lacore (14 days ago)
Who else is taking AP calc bc rn
Sarfraz Ahmed (20 days ago)
tnx sir
Ankit Arya (23 days ago)
i understood everything, thanks thanks personal notes for me... ----------------------------------- g(x) = y or y axis value in video, this is g(x) or y = { x^2 , x =\= 2; 1 , x = 2} this is a way of defining a function, here this one specifically means is if g of x or y is equal to x^2 then dont take 2 as the value of x, you can take any thing else but two. if g of x or y is equal to 1 at any point on function then value of x will be equal to 2 thats just how function is defined date: wed/sept26/7:12am
Josh T (26 days ago)
what. are. you. talking about. 0 over 0 is not undefined. 0 / 0 = 0 0 is the only number that _can_ be divided by 0 without resulting in an undefined value. -at least that's what i've always been taught, i could totally be misinformed-
Zero C1 (21 days ago)
Josh T yeah :d
Josh T (21 days ago)
Zero C1 oh i see where i misunderstood you now. basically, if x = 0/0, we can plug any number for x, and it's still true, therefor every number equals every other number and we break numbers. yeah that makes sense now.
Zero C1 (21 days ago)
Josh T my original comment was about 0/0 in general and not as a result of a function when a value is plugged in.
Zero C1 (21 days ago)
Josh T f(x)=17 is a function of x and no matter what value x takes it is equal to 17 and the graph would be a straight horizontal line parallel to the x axis.
Josh T (21 days ago)
Zero C1  but wait, isn't that true for any constant? if we were to say that f(x)=17, then no matter what value we plug in for x, it will still be 17.
ItsXabi V (26 days ago)
and i thought 2 + x = 1 is bonkers. btw i'm 15
Khail Anonymous (27 days ago)
sorry i can't learn about this because limits dont apply to me mic drop bruv
Joaquin Alejandro (27 days ago)
that really helps me thx
aasim memon (27 days ago)
is there any real world example where limit is used .. what is benefit of limit ?
Zero C1 (21 days ago)
aasim memon it helps us to understand and solve otherwise undefined terms and also its the basis of all calculus.Without limits there is no calculus
SoCal Justice Warrior (1 month ago)
Okay. This is epic.
Martin King (1 month ago)
Thank you, this explanation helps me understand limits :)
Shivangi Sharma (1 month ago)
Thanks sir u are really making students lives simpler with this amazing teaching of yours .
your not telling limit correct defination
Dima JJ (1 month ago)
i never struggled to understand anything in math. Except for this lesson. legit on my senior year my brain shut downs
kayley (1 month ago)
Why do you get 4 on the y axis at 7:07???
C0reInside (1 month ago)
Dhanak Kainaat (1 month ago)
Man Calc is hard😩
Nitish Bhardwaj (1 month ago)
it's a bund panga.
Prithvi Sundar (1 month ago)
The Youtube Tutorials are better than the app's
Prithvi Sundar (1 month ago)
Nice thank you
ILikeCycling (1 month ago)
i just want to cry :(
Miku Plays League (1 month ago)
I love this channel... It's so easy to understand. I learn so much from this channel, much more than my college professor. Thank you for pushing out such great content!
Tamara Nuñez (1 month ago)
Buen video Profe bonito fin
Noah Pillow (1 month ago)
10:30 shoutout to floats
Aabisheg Aabi (1 month ago)
Tq bro
mikhil shivaraman (2 months ago)
subito zx (2 months ago)
Tbh I’m surprised you do all these videos with a mouse. You could probably do it in half the time with a sketch tablet. It’s the thing artists use to draw digital pictures. It looks like an etch a sketch with a pen (not one of those tablet pencils, or magnetic ones). They are incredibly precise and I believe are wireless. Maybe I’m wrong and you do use one but I’ve always assumed that you’ve done so many of these videos you’ve just gotten really good with drawing on a mouse
sealofbeyond (2 months ago)
Actually, I think he does use a drawing tablet! :)
l Stylius l (2 months ago)
8:53 *nein nein nein nein nein*
Tin Chi Ng (2 months ago)
I dont understand the part X*2 =1 when x =2 how come ? OR it is just an example ?
Xochitl Vanessa Gonzalez (2 months ago)
So technically the limit has to be where the gap is at?
Bertold Szekeres (2 months ago)
Sorry, what's the function when x = 1 again?
Kancharana Sudhir (3 months ago)
Hugh Jass (3 months ago)
You must have captions in more languages
Rod Gabrielle Canete (3 months ago)
Ahmed Maazouzi (3 months ago)
It was actually a beautiful parabola.
My lectures is making it looks difficult and class so bored... Just find out from a friend and after watching few videos I think have leant a lot... Kudos Khan Academy...
Rumi Mollick (4 months ago)
free tuitions
Mansi Saini (4 months ago)
Trusty calculator wasn't really trusty
Ritam Dey (4 months ago)
Thank you sir....
insane everything (4 months ago)
Limit tends to boring
010011 (4 months ago)
he is confusing. follow a straight logic. don't be all over the place
010011 (4 months ago)
he is confusing. follow a straight logic. don't be all over the place
Acchan Kakkoii (4 months ago)
N there are still many people say that 'divided by 0 equals infinity' xD... Its only +-infinity if its approaching 0 from the left or from the right...
Jesse Gabriel (4 months ago)
Calculus is infact so easy - only thing is: thinking its difficult before even studying it
ankan choudhury (5 months ago)
extremely useful video.thank you !!!!!!!
Unlock Now (5 months ago)
It gets on my calculator : 3.9999999999999999999999999999996 4.000000000000000000000004 LOL ! Thank you so much for this video !
Dawson? (5 months ago)
Sylvester Stalone??? Is that you????
Azaezal belthood (5 months ago)
Ur so awesome
Sangita Biswal (5 months ago)
Thank u sir for ur teaching tutorial This helped my son a lot Thank j again
Andrew-Kitwana Mbogger (6 months ago)
6:18 hahahaaaaa
Arjun Misra (6 months ago)
Nice work
Sunando Mukherjee (6 months ago)
very useful
Sunando Mukherjee (6 months ago)
can anybody tell me the software used by sal
broncojonnes (6 months ago)
Real MVP
Dorian Gibson (6 months ago)
graph perfectionist
Anannyo Samayel (7 months ago)
If I ever earn because of your videos, I promise I will donate you guys $1000
Abhishek Kumar (7 months ago)
In hindi plzzzzz
Olerato Poto (7 months ago)
Best teacher ever.....you dont need to memorise the rules you just know them the way he explains
venkatesh nagarapu (7 months ago)
3.01 if the value is undefined, y we need to study and rub over it..... who invented this yaaarr irritated
Ryan Chiu (7 months ago)
0:16 Captions to many reallys
Marc Rindermann (8 months ago)
thumb down for arrow heads on both ends of the axes @ 2:08
ArthurHaXz (8 months ago)
G of x is a peicewise function right?
satyendar kumar (8 months ago)
pleass make it in hindi
TheProgrammingJedi (8 months ago)
Thank you!
Flaskie Flames (8 months ago)
Your voice really reminds me the face of Tom Hanks. My teacher haven't discussed yet about calculus but I'm really curious about what this.
blissful fragrance (8 months ago)
...Learning through khan academy seems very impersonal and distant, you know what I mean? I appreciate *all* the wonderful things they're doing for us. But they never reply to the genuine doubts people have.. I know they must get hundreds of comments a day but still.. @[email protected]
M S (8 months ago)
lmaoooo when he redrew the parabola
serden (8 months ago)
one point ninininniniinini... hahahah you are the best Khan.
EternalAbode (8 months ago)
I have some doubts...what are functions? Why do you apply limits to them for no apparent reason? And then try to get close to that limit, what’s the point?
EternalAbode (8 months ago)
Makes no sense...what can I get out of limits which seems no different than an insane randomly write unreasonable things and claim it to be science
wef (8 months ago)
MILLYEO TV (8 months ago)
immanuel neihsial (8 months ago)
Camille Lee Caguiat (9 months ago)
can u plss solve this problem: -prove that the function define by f(x)= x^n-1/x-1, where n ∈ z^+, has a removable discontinuity at 1.
Rovy Trinidad (9 months ago)
suppose that f(x) is continuous at x=0 a) prove that limit x->0 xf(x)=0 the converse of this statement is not true that is the fact lim x->0 xf(x)=0 does not guarantee that f(x) is continuous at x=0. find a counter example; that is b) Find the function f such that lim x->0 xf(x)=0 and f(x) is not continuous at x=0
corazon villanueva (9 months ago)
Can u plss answer at this questions: -use mathematical induction to prove that lim x ->a [f(x)]^n=L^n for any positve integer of n
B Siva venkata Nagaraju (9 months ago)
1-1/1-1 0/0 we cancel by both by 0*1/0*1 will becomes 1
Srivatsa Bolisetti (9 months ago)
9:08 why isn't it y=1? the problem says when x=2 y=1
Ross Nkama (9 months ago)
Its because x isn't 2 yet, x is approaching 2 and getting infinitely closer. So because the function condition that x=2 hasn't been met yet, y = x^2.
Mariella Perlas (9 months ago)
Hi. What application do you use?
Mariella Perlas (9 months ago)
Hi. What application do you use?
Mariella Perlas (9 months ago)
Hi. What application do you use?
Mariella Perlas (9 months ago)
Hi. What application do you use?
Patrick Brajeivik (9 months ago)
I hate Pre Calc and my teacher. like if you agree
John Myers (10 months ago)
iM CONFUSED... Why does the parabola keeps going if the limit of g(x) is 4? is it just because of a minor shit (meaning, that it skips 4 at g(x) ) or what?
The hardy boys (10 months ago)
The moment they started mixing letters in with the math was when it all quit making sense to me.
Alana Liu (10 months ago)
What is the line called that is graphed f(x)?
Gitender Kumar (10 months ago)
Tx sir!!!😊😊😊
Brock Lesnar7 (10 months ago)
He is a Genius .who accept me?
Paul Edsel Dastas (10 months ago)
That calculator is soo cute
sabir thara (10 months ago)
when will a ceiling function equal to flooring function
Vardan Ohanyan (10 months ago)
Should the function be discontinuous in order to have a limit?
Ronan (11 months ago)
You shouldn't be trying to learn this at a young age right?
Marbles (10 months ago)
Ronan well i am 😑
Denovo Tutor (11 months ago)
Sal you inspired me to start my Chemistry/Calculus/Physics Tutoring channel! Please check my stuff out guys
Sam Karki (11 months ago)
Very helpful. Thank you so much
saju janardhanan (11 months ago)
c l o u d h a i r (11 months ago)
I have a maths exam in 4 days and this really helped me understand limits, part of what my teacher calls: 'conceptual understanding' and expects us to know. Thank you so so so much.

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