Introduction to limits | Limits | Differential Calculus | Khan Academy

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Introduction to limits
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Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.
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Опубликовано:

28 сен 2024

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Комментарии : 1,2 тыс.

@jameserayburn 9 лет назад

I really enjoy a good refresher. My grandmother was a high school teacher for 43 years, so I know that it takes a great person to be a great teacher, and Mr. Khan is one of those few great teachers.

@shannenlibres2365 3 года назад

sorry to bother you can you explain to me why in 7:08 the gap/limit is on positive y4? how did he know it had to be on point (x2, y4)? I understand the x2 part but not the y4 part. Also why is it that we define the entire parabola as "x^2" (from x^2, x≠2) not equal to when 1 (from 1,x=2) is just the placement on the y axis? I hope I make sense please please help me

@afonsodeportugal 2 года назад

@@shannenlibres2365 It's been a year. Did you figure it out?

@nihilsinedeonihilsinedeo3137 Год назад

@@shannenlibres2365 because that's just how the function is defined. When x=2, in other words , f(2)= 1 not 4 because the value of the function when x=2 is 1. The x axis represents the values of x, the y axis represents the values of the function. Because of what I previously said , 4 can not be a value of x=2 , because f(2)=1 but can be a value of f(-2) because -2 is not equal to 2 , therefore f(-2)=4.

@LivingchurroBlogspot 8 лет назад

Not all heroes wear capes

@agustdel5571 8 лет назад

oh so true

@Rhyff 7 лет назад

How do you know that he's not wearing a cape? ;)

@hemiacetal1331 7 лет назад

Not all heroes wear underwear over their pants....

@JoeCnNd 7 лет назад

cool man!

@ieatbeans188 7 лет назад

some make calculus tutorials to save us from professors who don't even speak coherent or understandable English when that's the only language spoken by every student in the class.

@willr455 9 лет назад

Your parabolas are beautiful, don't let ANYBODY tell you otherwise.

@XerxesTata 7 лет назад

Real people don't judge a parabola by its curves, but by its personality :)

@SathvickSatish 7 лет назад

If anyone didn't get Red Wolf's comment, search up "There's only one true parabola" and click on Matt's video

@davidcooper2589 5 лет назад

@Teringventje Stfu

@dribbler456pls8 4 года назад

Benson luo when graphing quadratic functions you get a parabola this U shape

@ssin1785 3 года назад

@Ro beau graph of a quadratic equation

@wolfieswifty13 9 лет назад

You are a hero! I have a quiz tomorrow on functions, limits, and derivatives and I knew nothing! At least now I know the basics. Thank you so much.

@LearnMathsFree 9 лет назад

+Wolfie Swifty How did the quiz go?

@brandonstreets9177 9 лет назад

did you do well?

@kentbrantly8183 8 лет назад

+Wolfie Swifty Did you pass your quiz?

@K40TIKsPl4Yer 8 лет назад

+Wolfie Swifty We will NEVER know what heppened during this quizz

@e02_v41 8 лет назад

+Wolfie Swifty he prolly got a 60 or something, one video isnt gonna do shit to prepare for a quiz he doesn't know anything bout

@strangelilmei 2 года назад

Taking AP Calc AB this year. I'm absolutely terrified... but Khan Academy is truly a blessing and makes me feel more confident.

@jlogs872 2 года назад

fr dude... ap calc ab is saved because of khan academy :)

@g0rrg4lici0us 17 дней назад

@@jlogs872 did you pass?

@jacewilder9268 8 лет назад

im a junior this year and learned basically nothing my sophmore year so im spending my summer watching your channel and actually oddly enjoying actually understanding math and pre calculus

@theatagamer90 8 лет назад

same

@saraa4673 6 лет назад

you do calculus in junior year?????

@newq 5 лет назад

I never enjoyed math until Sal Khan came along.

@paaritoshsingh6427 5 лет назад

Yeah, we do calculus in our junior in year( In India at the very least)

@padmeamidala278 5 лет назад

saraa I did calculus junior year because I got ahead in math freshman year

@agustdel5571 8 лет назад

we need to understand that we are equally as capable of understanding something as our teachers but for knowledge to be transferred whole from one mind to the other, perfect communication is the key

@her4087 5 лет назад

When im frustrated and about to give up and i hear Sals voice its instant reassurance and calmness. The way he approaches all topics is amazing

@sumithadavid5841 9 месяцев назад

This teacher is definitely the god sent soul to help a million of students in maths. I wish I should have seen this channel earlier….

@dd317676 8 лет назад

when you don't even understand khan academy, you know all hope it's lost 😭😭😭😭

@relativemotion 8 лет назад

+Domonique Thompson Maybe you should revisit some of the lower level content first? Idk what to tell ya. I've gotten farther in mathematics via Khan Academy than I ever did in K-12 schooling (USA).

@Domieboy 4 года назад

at least im not the only one

@VinodYadav-se5dr 3 года назад

Same here 😭

@lordshalomdizon3217 3 года назад

😭

@shannenlibres2365 3 года назад

@@relativemotion can you explain to me why in 7:08 the gap/limit is on positive y4? how did he know it had to be on point (x2, y4)? I understand the x2 part but not the y4 part. Also why is it that we define the entire parabola as "x^2" (from x^2, x≠2) not equal to when 1 (from 1,x=2) is just the placement on the y axis? I hope I make sense please please help me

@Reivivus 11 лет назад

Yeah, you explained what my Calculus teacher confounded me with for 3 hours. I didn't grasp anything in that class today...but, you are a true teacher...not an expecter!

@williamj.stockich 8 лет назад

Calculus students don’t fret if you don’t grasp limits. They are only proofs that calculus is valid. Unless you are a mathematics major, you will only encounter limits superficially in other scientific courses. What you are being taught now was not developed until the 1880s. This means that all the progress with calculus from the time of Newton and Leibniz in the 1680s was achieved without any satisfactory validating proofs as to why calculus worked. Derivatives can be achieved according to a set of rules; integrals have fewer useful rules; limits have no rules. Each limit problem requires a different approach, and examples provided are usually too simple to help. When you reach the point of not knowing how to proceed, you are in a pool of millions. Don't get discouraged, the rest of calculus is much easier to understand.

@binzsta86 8 лет назад

I'm not discouraged now, but will be when I bombed my exam.

@rachelpilato6474 6 лет назад

THANK YOU! Starting calc in about a month and haven't done precalc since 2006 and I'm FREAKING THE HELL OUT and trying to determine what to focus on for review.

@eldersprig 6 лет назад

There are 3 or 4 texts on infinitesimal calculus which go directly to the definitions of the D, by augmenting the Reals with infinitesimals. They then put 150 pages on limits into the appendix, but that's neither here nor there. Fluxions (infinitesimals) are intuitive but had no rigor, and it took a few centuries for someone to put the rigor into them, but then the damage was done so we're stuck with limits.

@gia2371_b 2 года назад

Comments 7 years ago: “omg thank you for saving me i have quiz tomorrow” Comments now: “oh look dapz just ratioed khan academy”

@henryconner780 4 месяца назад

This dude has spent thousands of hours helping students of all ages for free. Bro IS philanthropy

@echoesofsilence22 Год назад

Really, I'm in the 9th grade and finished watching this video with a basic knowledge of calculus. Thanks Sal, you're a hero.

@maxgeorge1463 Год назад

ummmmm... yeah this isnt an intro to all of calculus buddy. This is a good fundamental of calc, but only a raindrop in the ocean of calculus. Watch 3Brow1Blue's vid compilation on calculus. That vid series pretty much introduces every large concept youll learn in Calc 1. Limits barely introduce applications of derivatives and integrals.

@ricardomilos1784 Год назад

have you completed all calc classes?

@maxgeorge1463 Год назад

@@ricardomilos1784 ??? All Calc classes? Specifications please

@mesqueunclub101 12 лет назад

SAL! Seriously i dont know how i would have made the exams without you! I am sure to pass Chemistry and calculus becouse of u. I am sure to pass biology, if i watch all of ur videos about biology! I owe u big time! Tnx man!

@TheSuperkiller14 7 лет назад

This guy is a legend. You really do deserve an award :)!

@GjerdanPeterson 10 лет назад

the first example would've been easier to understand if both of the variable x and y were not 1 cause that confuses people...

@topnaman2735 7 лет назад

I agree to that

@adenc.9048 6 лет назад

Or if it was x-2/x-2

@alexpena9927 4 года назад

this stuff is a life saver when calculating time complexity in my computer science courses

@awesomecake_abc2748 2 года назад

how can i use this to find when my dad is coming home?

@theonlyalys Год назад

I'm just leaving this comment here so that after sometime when I look back on my past self, I remember the soul of that 10th grader who had just entered eleventh and found that it was not necessarily what they had always thought it'd be but something worthwhile at least and something that'll remind them of the rawness and beauty that once existed in life. So long, me.

@slothguy5716 8 лет назад

Watching these is the best way to review for an exam.

@obisvanainobis9950 Год назад

I am happy to say that while I was absoloutley confused on what a limit was I finally had some idea on the topic by the end of the video

@AG-po7bl 8 лет назад

Brilliant explanation! You are a really talented teacher.

@shivangi3030 6 лет назад

Thanks sir u are really making students lives simpler with this amazing teaching of yours .

@mukhzarramaalik6349 5 лет назад

This lecture is really helpful. Thank you so much

@TheGreatBrendon 13 лет назад

Sal, you are the greatest teacher there is, thank you for all your time.

@_____________5977 4 года назад

really really really SIMPLE idea. If it is that simple I won't be here watching your videos after my college class....

@Blap7 Год назад

"let me bring up my calculator" >brings out working photorealistic 2d TI-85

@caleb461 8 месяцев назад

Hey Sal, you might consider using an integer other than '1' in the function for your first example (e.g. (x-5)/(x-5)) to avoid confusing the function's output ('1' for all inputs except '1') with the function's input. Otherwise, the statement "f(x) equals 1 for all values except 1, but f(x) cannot equal 1 when x=1" can sound a little confusing.

@ThatGuy-kf5kc 11 лет назад

I'm learning limits in my Calculus class, and I don't understand it. You're helping me a lot! Just subscribed :D

@Blood-Lord 11 лет назад

Thank you so much for this video. Just because of this I have subscribed to you for future references for my class.

@natalia4903 4 года назад

thank you for being the first one to actually make this make sense

@nickioli13 9 лет назад

One point nien nien nien

@braisfernandez5687 6 лет назад

NickioliRavioli lul

@dimajj1840 6 лет назад

i never struggled to understand anything in math. Except for this lesson. legit on my senior year my brain shut downs

@souvagyapaul8989 2 года назад

Thank you so much for making the concept of 'limit' so simple as well as interesting for me🙏❤️

@martinrking 6 лет назад

Thank you, this explanation helps me understand limits :)

@charlescooper1664 3 года назад

I have a question about an example but forget about that. Your teach method is awesome

@m8sonmiller 11 лет назад

Jeez, we've been dinking around with trigonometry in pre-calc for weeks. At least now I can figure out what the Hell calculus is when they get arounfld to teaching that. Thanks Saul!

@jacklorenzrivera655 5 лет назад

Thank you! This is really helpful!

@kod3619 3 года назад

stop reading the comments and pay attention

@Mulkek 3 года назад

Awesome explanation!

@gaminglovers3097 5 лет назад

The video is super awesome

@UmerKhan-sk2lt 5 лет назад

Sir u r doing a great job

@uselesstaco7221 4 года назад

I am getting closer and closer to passing my calculus test.

@mel-dq1vk 4 года назад

time to relearn all of calculus in 2 weeks for the AP test, because I just realized I didn't retain anything this entire year. ready for death.

@liza_eajero 2 года назад

im actually trying to advance study and listen to a discussion but im quite disturb of the word "getting closer and closer" it just kinda make me more confused cause the word closer is always repeating and just kinda giving me more confusion. However its good, i like it.

@shockerjason 11 лет назад

How have you not won a Nobel Prize yet? *Serious question* We love you, Sal. I'm sure you know that, though. Thanks a million times a million and one.

@Swedishpersondude 13 лет назад

Its fun to learn from you!

@عازفالنايات 6 месяцев назад

Actually I learned that at college, but now I got the idea, thank you so much

@alyciamg 4 года назад

Sal!! Do you know what the “limits game” is? If you do could you explain it? Or define it please, the main concept please

@samrakshankarki 7 лет назад

Very helpful. Thank you so much

@tahabenly 10 лет назад

this video made me sleep ! no lie

@cundrite 11 лет назад

Hello, your video is very vlear, thank you. What software did you use to write directly handwriting? Thaks a lot for you answer, it would be very usefil to me!

@raredragon 9 лет назад

I am looking forward for more videos of you sir khan. I am now entering the world of calculus and may God Bless my subject grade for this. Not a college student but a high schooler so it would be very difficult i think?

@adnankhan96323 Год назад

Hope you are in university now . Did you learn calculus ?

@raredragon Год назад

@@adnankhan96323 im already an engineer :D

@TheImpressionable 13 лет назад

Khan, if f(1) = 0/0 is undefined, does that mean f(0.9 recurring) is also undefined because 0.9 recurring is equivalent to 1?

@olesya1388 10 лет назад

The limit does not exist

@curiositystranger5112 4 года назад

I am a class 8 student and I find all my acaademic math really easy and lame. When my friend told calculus as hard i thought it is actually easy for me. But its challenging and I am trying my best to understand.

@l3ertuz362 10 лет назад

any example of practical application of this?

10 лет назад

develops logic thoughts

@eduardofcgo 10 лет назад

This is the basic of calculus. Calculus is used everyday. You can build planes, computers, send shit to space and other important things our socienty does. With calculus you are able to describe the universe where you live, and solve almost any time of complex problem.

@MelissaR-cq7jj Год назад

Thank you thank you thank you omg😭😭 I was abt to have a literal breakdown over this

@corazonvillanueva398 6 лет назад

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

@surgicalmaterials 2 года назад

Im not even supposed to be learning calculus right now, i’m supposed to be doing my decimal homework, but here I am.

@SuperYoonHo Год назад

thank you

@johnnyrichards5211 9 лет назад

This is sooooo easy im in 8th grade taking pre-calculus and want something harder plz

@arpi6054 4 года назад

You’re a real hero, Sal

@Reivivus 11 лет назад

Do always "square" the closer numbers to the the actual limit? Or would you might "cube," in this case 1.99999999999 as in 1.9999999999^3...if your graph is cubic or even...what about a sine wave?

@kagisomarvinmolekwa3933 5 лет назад

what's the name of that program that he's using to perform all of the drawing? I take it the calculator is part of it?

@GrandGobboBarb 11 лет назад

What software is this? It looks AWESOME!!!!

@nguyentt010 10 лет назад

I hate limits it so confusing.

@srishtidotcom 3 года назад

6 years later and nothings changed

@shancunma6001 6 лет назад

This guy should seriously be nominated for the Nobel Prize.

@hankc6208 Год назад

Stfu Nobel prizes don’t work that way

@stefanihillrich4600 11 лет назад

Khan Academy, saving math grades since 2006

@gabrielfimbres8726 11 лет назад

I agree sal you should get a nobel prize thank you so much for all the knowledge you are putting out for free for everyone

@Lovechild4u 10 лет назад

I don't understand how this video topped over a million views. all he did was write on a glow in the dark board. Why can't you put it in an easy way so, that people can try and understand the purpose of limits and what ways to look at it from. Whenever a question says "approaching" it's wtf which way do I look at it from.

@animore8626 7 лет назад

For one, if you think that it's not easy to understand, you are in the minority. Just check the comments; clearly his way of teaching is beneficial to many people, and if you do not feel the same, I'm sorry. Nevertheless, you make quite the sweeping generalization. As per your question about limits, if not expressed specifically, we look at it from both sides. If the limit is not the same on both sides, we say it does not exist. I realize this comment is two years old, btw.

@mr.sundar8220 6 лет назад

The RU-vid Tutorials are better than the app's

@teachme_hub9399 7 лет назад

Nice nice nicw video by khan academyReally niceThanks fir making learning easy

@joeljose1737 7 лет назад

thanks .....it really helps

@danieljackson3981 4 года назад

6:32 when he kept redrawing it had me laughing 😂

@parasrocks52 10 лет назад

Thanks for all ur videos. They rock and you rock

@darkzonegaming9169 2 года назад

wow. i got it

@doriangibson8108 6 лет назад

graph perfectionist

@wajabi 8 лет назад

I start a Pre Cal course on the 27th, hope I can do well.

@davidkolek7913 8 лет назад

+Ezequiel Pereira Have fun, My Pre-Calc final is on the 27th...

@wajabi 8 лет назад

+David Kolek wish you nothing but the best David

@eliecerecology 9 лет назад

Why do we need to find limits? why practically I mean?

@joshuapoon2014 7 лет назад

When you're a professor and you teach it to students and you earn money to make a living Or you're a student and you want to graduate from uni or get a major in mathematics Or you're a mathematician doing mathematical research But srsly when was maths practical?

@HilbertXVI 7 лет назад

Joshua Poon Forever?

@joshuapoon2014 6 лет назад

forever?

@TheGoodvibezz 8 лет назад

How is the limit of F(x) = 1 if "x" cannot be 1? Does this mean that the limit is any number that would make f(x) undefined

@mrfrankincense 13 лет назад

0/0 certainly is undefined and so is 0 * n, infinity/infinity and infinity * n.

@DullDieHard 12 лет назад

It was something like " I wish this was 5 minutes long, it's too easy for me."

@IncognitoUser12 4 месяца назад

1:21 The real professional's word.

@matt-g-recovers 3 года назад

Makes sense except the part where G(x) all of a sudden leaves this natural arc for a value (1) not on the line?

@starlikeguy 3 года назад

Thank you very much

@vardanohanyan8605 6 лет назад

Should the function be discontinuous in order to have a limit?

@ehlee5394 4 года назад

i love how bothered he is w getting the parabola right. a king.

@Dazzling.R 3 года назад

I’m here in 2021 watching this hoping i pass Calculus after I drop it.

@theresehoven1137 7 лет назад

Question- 2^2 =4, so is the only reason that (2,1)happens is because of the limits of x=/2 and x=2 ?

@vtron9832 7 лет назад

Is it normal that I'm learning this by homeschooling myself while I'm in the eighth grade?

@nono-hmd-9982 7 лет назад

Alef Nol kudos to u ! this is not normal but genius.. people like u grow into smart somebodies and have lots of accomplishments

@vtron9832 7 лет назад

Thankyou

@goodtoseeya1543 7 лет назад

I don't think so

@theredstonehive 6 лет назад

I am trying to learn this by homeschooling myself in 7th grade.

@frogger832 13 лет назад

WHY CAN'T ALL TEACHERS BE LIKE YOU. WHY WHY WHY WHY WHY !!!!!!!

@Happy-em9xz 2 года назад

Fun fact: your here because of Dapz

@vijaykumarjha7822 2 года назад

Nope, i have father

@ElGuapo96 2 года назад

@thatmemestar378 11 месяцев назад

I came here to invent more mathematical equations for my science field of video editing 😂

@mayaanantharam6185 5 месяцев назад

Who tf is Dapz

@shanaya9876 Год назад

This 12years old video saved my semester 🙃

@AFIG92 10 лет назад

If you can't understand limits...go work at mcdonalds

@JayWerx 10 лет назад

LOL,I know successful investors that dont know any of this shit.In fact, I know lots of successful people in many fields you have no clue about this.I wonder what you do for a living and how much you make.Bet you dont make shit.Calculus has nothing to do with income potential young man.

@AFIG92 10 лет назад

Investment banking