Introduction to limits 2 | Limits | Precalculus | Khan Academy
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- Опубліковано 29 вер 2007
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Introduction to the intuition behind limits
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Those who are watching this after a lecture : RESPECT
Those who are watching a day before exam: I can totally understand
What about those who are watching before the lecture
Me watching this and going to learn it in 2 years ._.
@@DrowQ you are a prodigy man
I am watching this cause I am curious about the topic of calculus
You got me
890,000 views. The most attended first year Calc lecture to ever occur.
Nicholas Jones 1.5 M
1,589,833 views now
1.6+ M
now, as i have noted the + sign, dare beat me!
Like if in 2019 and taking calculus 😂
1.7 Mill. in sept. 2k19! 😀
Nice to know I have 1.5 million buddies who also don't understand Calculus.
Ha, never stop learning im 44 and i dont know it
Im taking it this year and I hardly even know what its about
@@frank-ts1yr You gave me hope.
😂😂
Hmmmm 5537238 iota
A limit is a definite number. I'll do a video soon on the rigorous definition of a limit.
ok
Ok... Noice one
Woah i would have failed my school if it wasn't for you sir
Sir.. I can't explain in words my gratefulness towards you... Wish you will be continuing to guide us like this ❤️🙏
Wow 14 years ago.... Still helps
You made history haha
I'm watching this video in 2023. But there's nothing surprising that this video is still useful as it's made by most honorable person. Also watching this video inspired me how small things turn into invaluably precious things by making heartly efforts in right way. The way that Sal started deliberately on his small computer with incredibly low resolution inspires millions of common people worldwide to startup new things in their lives. Special thanks to the one and only real educator -'Sal'.
me also
this crap is a life saver, i don't learn shit in my actual class, but the combined with the text book and friends is the only way i can learn anything. And some how this actually makes it easy for me.
Actually I do things the same way
*this grap
Me who is 14 :)
I'm calling holes "graps" for now on :D
Do you still call it graps?
4:37
i just imagine sal coming home after a party and it's 3am and he just thinks
hey, let's make a calculus video.
for all of those whom don't get why lim f(2) is 4: My teacher always told me the limit is the number the graph is trying to reach. as you infinitely get closer to 2 on the x axis, the graph Is trying so hard to get to 4. due to the explained circumstances, the graph itself does not go through 4, however, that's what it's trying to reach.
Thanks mate for ur kind explanation!!! Now I think I can define it in my own words..
*who
i'm a visual learner and that helped a lot
How about when lim f(3) ??3 on the x axis?can someone expains?
@@syafiqadly9428 9 as there are no obstruction mentioned like x does not equal to 3, therefore x^2 = 3^2 =9...I'm fairly new to this topic but that's how far I understood
dude. thank you so much. i'm just starting calculus and was already freaking out (today was literally our first class and just review and an overview). now that i've watched this video it's calmed me down a lot; i feel ready for tomorrow's class. thank you! :)
Wow how industrious you are, to prepare for a class like that. I'm literally watching this bc I have midterms tomorrow and I don't know a thing.
6 years later and students (like myself) are in your exact same spot. I can only hope it went well for you and that it will go well for me also
How was High School and University or College for you? It's been 8 years since this comment, I was only 10 at the time.
@@Arthur-fs5vl this is such a sweet comment! switched into the arts because calculus was not for me (as the comment 8 years ago implies), much happier now and making lots of art! hope it goes great for you too :-)
@@sophc193 Thank you very much Sophie, wish you the best in your future art projects and God bless!
it's crazy how you've helped millions of students, including myself
thanks
And now the number became a billion
It's crazy to find old comments, when people wasn't as fake as now and they showed their real opinion
👏
You have the concept absolutely right. I think it is just the notation that is confusing, particularly since the notation uses an = sign. But what the notation means is as the graph approaches x=2 the y values will get closer and closer 4, but never reach it (until x=2). In other words, the limit is the number that the function is heading to as x gets closer to 2 (or whatever number we're interested in). I'm sure you've figured all this out by now, but maybe it can still be helpful to someone.
5 yrs later, very helpful to me. Thank you very much
9 years later helpful to me
I think it's great that you keep showing students how the functions relate to the graphs instead of just showing them separately. It made limits feel a lot more intuitive to me. :)
wouldn't it have been cool in school if our blackboards used neon colored markers. It makes for a better presentation. (yes i realize that this is not with markers but a comp program)
We have a smartboard in our class and it looks almost similar to the video when something is written on it .......but the background looks dark(darkest?) green instead of black and it doesn't look good. LOL .......Honestly i feel there is something satisfying about the creak of chalk while writing that makes it special 😅
I just want to say that Sal is an great teacher. I'm a college calc I student who is REALLY bad at math and I am pretty sure I'm going to pass my calc class thanks to this guy! (Final is tomorrow...wish me luck!)
Did you pass?
are you even alive bro ?, it has been 13 years
Bro you alive?
How's life going?
Bro, This video is one of the oldest videos we have. Its a treasure.
_grap_
Haha love your efforts and amazing explanation.
You've definitely changed the education system for real, one of the few golden drops here. ❣️
lol I was about to comment that and saw your comment🤣
I don't know if youtube pays you or not and because some of us cannot afford to donate we can definitely watch adds! please go ahead and add at least two adds in your videos to support fundraise!! Thanks, soo much from Pakistan!!
I just want to thank you so much for your effort in helping others. I can use your videos for all my subjects and get so much more out of them than being in class or reading a textbook. I was so stressed out before discovering your channel. You are amazing!
It's been a good semester Professor Khan. I've come so far since watching this video an hour before my first Calculus exam. Brushing up for my final, just wanted to thank you for all the help getting me through this course.
I was in first grade when he did this video. Here I am, 13 years later and its still so helpful!! thank you Sal.
calculus is not hard but very time consuming.....i really appreciate your videos and i rate them 5/5 without a doubt cuz they help me so much....may god bless u men...
omg a grap
I'm a Marine stationed in North Carolina, I'm heading back to college after my training and I needed a review of Calculus. I can say you explain this subject as consise as a college professor would, you've done a superb job and I laud you for it sir.
how did college go bro?
@@tvsked it has been 11 years i am curious too🤣
Thank You Man... YOU ROCK, I have been sitting in my cal one class for over a month, and did not understand what a limit was or how to evulate one until this video... YOU Rock! If I ever hit the lotto, I'll be sure to compensate you!!!
thank you thank you thank you thank you thank you. I have ADD and although I loved how simple and easy to understand Calculus For Dummies was compared to my brother's college textbook, it's still a book and I quickly get bored and leaving. These videos are wonderful and I will be comming back for the whole series and perhaps for the physics and chemistry ones as well.
Great work! this should really help me prepare for pre-calculus, which have to take online over the summer
Sal, im 18 fresh outta high school and already joined the nuclear program with the united states navy. Im shippin out in oct for boot camp, then going to school to learn every thing a nuclear engineer needs to know. I plan on using your videos when im syumped. Also, i would not be suprised at all if you (salman kahn) recieves a nobel peace prize one day to come. Please, keep making the world a better place with your videos! Thank you so much.
When this video was made I was at preschool .... But 12 years later I am still enjoying the works of Sal 🔥🔥🔥🔥🔥 Well Done
you rock, you have saved my life dude.... thanks from Buenos Aires, Argentina!
marvellous..now I am confident enough to take tution for highschool kids on limits
AweSOME man - love the drawings , hehe "a grap in the function" - Keep the limits, derivitaves coming .
My precalculus course have a more complex version of the limit notation at the beginning of the course. But his have helped me quite a lot. I love math 😄
Btw great video! wish all teachers were as helpful as you!!!
Now 964,000 views. Let's push it to the 1,000,000 mark.
+Michael Nguyen 995,000 SO CLOSE
+Michael Nguyen we did it
+Michael Nguyen I honestly wish the views started reading 999,999.9 recurring.
PUSH IT TO THE LIMIT!
Scarface approved
lol i am reading this now in 2018
thanks for this presentation ur explanations are always carefully thought out and make sense
I really appreciate you Sir for your immense help to all our maths needs... You've also inspired me to make my own channel.. I've uploaded some more questions which could also help those looking here for help
It helped me a lot..I am really grateful that I got your video or eslz I would have failed in my test.
I learn more from these videos than I do with the videos provided for my class.
This is why I didn't go to college. I'm a pretty good software developer, and I completely understand this concept. What I still don't get is the "why" part - the application of this. Even a few brief mentions of where this actually applies, where it is used, would be so helpful for it to click with me. I totally get the concept, no problem, but I'm just absorbing knowledge at this point, but not able to truly fully take it in yet. I'll keep watching the series and hopefully it will make more sense.
wow these videos are great! please keep them coming
Your voice was much better than the previous vid.
i watched this video and went for my math exam .. it really helped .. good job man.. thanxxxxxxxxxxxxxxxxx
Thank you for the video!
Thank uuu, it really helping meeeee
Why does he sound so happy at the beginning?? XD
He loves Limits dude.
jounynFM funniest, best timed comment on youtube :D, it's totally viable he loves limits that much :D, it's Sal after all :D
jounynFM Too much. Not needed to understand calculus.
Loving these videos!
Omg! I wish I knew about Khanacademy a long time ago! It would of helped me out so much!! Dx
Great explanation..with a good sense of humor..thanks
sal is an amazing teacher
This man actually made studies a real gift for everyone
I am finally going back to college since math was my least favorite subject thanks to you Salman!!
i like this guy. this will be awesome for calc 2 next semester. YAY :)
mind okay up until 3min mark mind blown at 3:10 and beyond... great videos on how you explain this. I am eternally grateful
Great way to teach limits and calculus.
Thanks that was helpful 😃
Awesome explaining and funny too. Thanks dude!!!
Awesome teaching skills..
Thanks for the video.
Dana
thank you its all clear.
oh, i already took cal 1 (actually it was AP Calculus AB). limits are like the first thing. :)
what i meant was this whole series on calculus will be useful in cal 2. i hope it covers some of that stuff, but even if it doesn't this is still really great for review.
Im from Brazil and Im just starting calculus. I attend civil Engeneering and i am so exited and nervous and such fritened.
Actually, I had to start over. So, I am attending calculus 1 again. And this time I hope I'm gonna succeed.
+Sergen Yurdakul good luck for you dude! We'll gonna succeed. ;-)
+Guilheme Wallace According to my experience. If you stick too much to the proof of the basic equations and thinking why they're that way, instead of accepting them just like that and use them for calculation. It'll be hard to pass.
Ann Schreiber yes, you're right. I also think that we should only do math the way it's supposed to do, not asking why, why, why. But I think this time I'm going better, I've just took my second test and think I was successful. ;-)
***** sometimes I think it's like this. It's very hard to understand every details while we have a lot o things to learn and a lot of matters.
*Loved the ‘grap’ joke*
hey you have inspired me to make my own educational videos :) and i have, on calculus
thanks a ton :D
i started to love math again :D
Thnx bro. As always great video.
wow that was interesting thank you!
Great video very helpful.....
I love you Khan!!!
Do limits always have to be values off the y-axis? Just for verification, limits are numerical values that a function approaches but cannot equal to?
The voice is nice and explanation is good.
Push it to the limit! This song just popped into my head lol
you are the best thank u for ur time god bless u
Thank you so much sir ❤
haha.. gap in the graph = grap
This is awesome.
The concept of limit is relatively simple but people find it very confusing, I will tell you why. Most of people think that functions have a single expression in other words they think that functions are only elementary functions (polynomials, trigonoemtric, exp,... Etc or combination of them). The concept of function itself is not well explained in books so people say why in the hell we have to invent the concept of limit at all if we have just to plug the number in the function and evaluate it. In short in mathematics the concept of function is more general than elementary functions. In most applications we are familiar with basic functions. I remember once when I saw a function defined as cases (multiple expressions) I thought that is not a function but mathematically it is a function.
wow, i love your videos and my whole family does too!
Well done !!!!
Thumbs up for those who see this videos day before the exam.
U r just too good at making though look easy
Watching this after 14y of release, 5y after taking my first calculus class, just brushing up concepts
Thanks for the videos.
Sorry,what kind of tools or software that you used to make these videos?
Thanks.
THE GRAP THING WAS HILARIOUS!!
I think what makes it harder for people trying to do it in quiz's is because they don't exactly have all the answer choices to begin with first time watching this video never knew it was so simple
Thank you so much
thx this is great
Thanks for the videos man. Hopefully I'll get a 4.0 in calc =)
THANK YOU!!!
@TeleMentoring I love Sal's videos and mission. I will be happy to transcribe out some of the videos and Email the words off to whomever. It just has to wait until after finals.
I watched this and realized that I already knew how limits worked and what they are XD As soon as you wrote down the example, I blurted out "4".
Same
谢谢, 真好:D
What field uses these functions? I'm a draftsman for an engineering firm, and with all the math I use on a daily basis, I've never seen these functions used.
I don't know that any field uses these directly, but these are foundational to higher level maths that I do use in various types of computing.
Chemical engineering.
Am also a draughtsman maybe we can just use the graphical approach and leave the analytical analysis for them lol
Trigonometry uses limits more than calculus but its not a field
What happens with the f(x)=3 when x=2, is it not considered in the limit? Just for graphing purposes
You dnt knw he much your videos have helpd me Sal.
I m so glad i found you on youtube....^_^
We have a grap! Lol. Hey, this vid really helped me. Thanks dude! Keep pumping out vids :D Thanks Salman.
sal should get a noble prize for how many students he helped.
Thanks!
That was amazing
Grap, thats an interesting concept :)
its of gr8 use :)