# Introduction to limits | Limits | Differential Calculus | Khan Academy

10598 ratings | 3890720 views
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Brian mutanya (18 hours ago)
May God continue blessing you sir i understand alot of things
Thank you! This is really helpful!
MUSIX-FREEZE (9 days ago)
Thanks For Educating Worldwide! You Are My Favorite Personal Teacher! You Basically Have The Coolest Job!
narayanan lakshmi (11 days ago)
💖👏👏👏👏👏
Nirupam Sinha (19 days ago)
You are best. Now I know what limit is but could not get it reading my book . Love you sir😍
Nice
Excellent
Kaan Inal (20 days ago)
Türkiyeden gelmişem altyazı yazanın ellerine sağlık
Sumaiya Fathima (22 days ago)
Oh l am a ultra genius who dont need to understand this limits😂😂😂 cause I can't understand this limits 😂
Raj (22 days ago)
Me: I'm failing calculus Sal: I'm gonna stop you right there
gsrini (27 days ago)
Now I have a limited understanding about the limits
Math lover
Umer Khan (1 month ago)
Sir u r doing a great job
mridula narjinary (1 month ago)
The digital calculator, how and where did you get that Mr. Khan?
Mukhzarra Maalik (1 month ago)
This lecture is really helpful. Thank you so much
Amazing 😍
CJ LT (2 months ago)
I think 0/0 is indeterminate
Divaliciousbeauty123 (2 months ago)
Calculus makes me physically ill
srinuallena (2 months ago)
The concept could have explained much better than this.
Nitty Gritty (2 months ago)
The limit doesnt exist
Sabbir Ahmed (2 months ago)
You need to add bangali caption
jesse cole (2 months ago)
*year old kid

This guy should seriously be nominated for the Nobel Prize.
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 (3 months ago)
💚
zoraiz ahsan (3 months ago)
good job khan G
the direct girl 123 (3 months ago)
at 9:13 he farted i swear 😂
Ishant Sharma (3 months 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 (3 months ago)
Who else is taking AP calc bc rn
Saiful Islam (3 months ago)
tnx sir
Ankit Arya (3 months 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
Jay (3 months 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 (3 months ago)
Josh T yeah :d
Jay (3 months 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 (3 months 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 (3 months 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.
Jay (3 months 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 (3 months ago)
and i thought 2 + x = 1 is bonkers. btw i'm 15
Khail Anonymous (3 months ago)
Joaquin Alejandro (3 months ago)
that really helps me thx
aasim memon (3 months ago)
is there any real world example where limit is used .. what is benefit of limit ?
Zero C1 (3 months 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 (3 months ago)
Okay. This is epic.
Martin King (3 months ago)
Thank you, this explanation helps me understand limits :)
Shivangi Sharma (4 months ago)
Thanks sir u are really making students lives simpler with this amazing teaching of yours .
nutulapati v.s Venugopal (4 months ago)
your not telling limit correct defination
Dima JJ (4 months ago)
i never struggled to understand anything in math. Except for this lesson. legit on my senior year my brain shut downs
kayley (4 months ago)
Why do you get 4 on the y axis at 7:07???
C0reInside (4 months ago)
one point NINE NINE NINE NINE NINE NINE NINE NINE NINE NINE NINE NINE NINE NINE NINE NINE NINE NINE NINE NINE
Dhanak Kainaat (4 months ago)
Man Calc is hard😩
Prithvi Sundar (4 months ago)
The Youtube Tutorials are better than the app's
Prithvi Sundar (4 months ago)
Nice thank you
ILikeCycling (4 months ago)
i just want to cry :(
Miku Plays League (4 months 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 (4 months ago)
Buen video Profe bonito fin
Noah Pillow (4 months ago)
10:30 shoutout to floats
Aabisheg Aabi (4 months ago)
Tq bro
mikhil shivaraman (4 months ago)
1.99999999999*1.999999999999=3.9999999998
subito zx (5 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 (4 months ago)
Actually, I think he does use a drawing tablet! :)
l Stylius l (5 months ago)
8:53 *nein nein nein nein nein*
Tin Chi Ng (5 months ago)
I dont understand the part X*2 =1 when x =2 how come ? OR it is just an example ?
Xochitl Vanessa Gonzalez (5 months ago)
So technically the limit has to be where the gap is at?
Bertold Szekeres (5 months ago)
Sorry, what's the function when x = 1 again?
Kancharana Sudhir (6 months ago)
I
FracturedButWhole (6 months ago)
You must have captions in more languages
Rod Gabrielle Canete (6 months ago)
DZE LIMIT DOES NOT EXISSTT!!!!
LIVINGSTONE OTIASAH (6 months ago)
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 (7 months ago)
free tuitions
Mansi Saini (7 months ago)
Trusty calculator wasn't really trusty
Ritam Dey (7 months ago)
Thank you sir....
#INSANE EVERYTHING (7 months ago)
Limit tends to boring
010011 (7 months ago)
he is confusing. follow a straight logic. don't be all over the place
010011 (7 months ago)
he is confusing. follow a straight logic. don't be all over the place
Acchan Kakkoii (7 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 (7 months ago)
Calculus is infact so easy - only thing is: thinking its difficult before even studying it
ankan choudhury (8 months ago)
extremely useful video.thank you !!!!!!!
Unlock Now (8 months ago)
It gets on my calculator : 3.9999999999999999999999999999996 4.000000000000000000000004 LOL ! Thank you so much for this video !
Dawson? (8 months ago)
Sylvester Stalone??? Is that you????
Azaezal belthood (8 months ago)
Ur so awesome
Sangita Biswal (8 months ago)
Thank u sir for ur teaching tutorial This helped my son a lot Thank j again
Andrew-Kitwana Mbogger (9 months ago)
6:18 hahahaaaaa
Arjun Misra (9 months ago)
Nice work
Sunando Mukherjee (9 months ago)
very useful
Sunando Mukherjee (9 months ago)
can anybody tell me the software used by sal
broncojonnes (9 months ago)
Real MVP
Dorian Gibson (9 months ago)
graph perfectionist
yg pol (10 months ago)
If I ever earn because of your videos, I promise I will donate you guys \$1000
Abhishek Kumar (10 months ago)
In hindi plzzzzz
Olerato Poto (10 months ago)
Best teacher ever.....you dont need to memorise the rules you just know them the way he explains
venkatesh nagarapu (10 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 (10 months ago)
0:16 Captions to many reallys
Marc Rindermann (10 months ago)
thumb down for arrow heads on both ends of the axes @ 2:08
ArthurHaXz (10 months ago)
G of x is a peicewise function right?
satyendar kumar (11 months ago)
pleass make it in hindi
TheProgrammingJedi (11 months ago)
Thank you!
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.
M S (11 months ago)
lmaoooo when he redrew the parabola
serden (11 months ago)
one point ninininniniinini... hahahah you are the best Khan.
EternalAbode (11 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 (11 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 (11 months ago)
One point NEIN NEIN NEIN
MILLYEO TV (11 months ago)
brah
immanuel neihsial (11 months ago)
Good
Camille Lee Caguiat (1 year 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.
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 (1 year 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