Limit examples (part 1) | Limits | Differential Calculus | Khan Academy

[@Peter_1986]

A lot of math teachers also have a tendency to be extremely vague about everything. They will throw out formulas and crap all the time without ever explaining WHY they work. That's exactly what Khan explains in all his videos, which is a big reason why he is so awesome.

[@BizzNitzz]

My Physics teacher once told me a good quote and my History teacher told me the same one 5 hours later, it went a little like this: "Teachers are the biggest barriers when it comes to learning."

[@krabmeat921]

Literally my math teacher bro

[@mikeo.4203]

Literally explained everything in 7 minutes what took my professor 2 lectures...

[@SarinaSaman]

This was updated 2007,, & I'm learning from it in 2017,,, thanks Khan Academy for being there when school can not help..

[@ajarofweed2181]

And me in 2022

[@saratvchannel5638]

2023

[@aryanrajput1841]

Me in 2024

[@hi-z]

why am I paying so much money for college if I can learn the content more easily on KZbin. sigh

[@ThefamousMrcroissant]

+Rare Pepe I'm going to try that from now on too. Especially during physics and linear algebra

[@hi-z]

I'm in college bro, wtf is wrong with ME

[@jackjiang7535]

+Omarr Omar we took this in grad 10 in China. U are lucky bud.

[@Egyptbalti]

+Omarr Omar haha me too, Omar xD

[@ThefamousMrcroissant]

Jack Jiang Stop talking shit

[@93stormer]

When I arrived in college, my professor automatically assumed that I remembered EVERYTHING from all my past math classes. Sure I could factor and use trig functions, but I don't remember what I don't use. I was lost when we started on limits, until I saw these videos. Khan at least doesn't automatically assume that you remember everything. His style allows you to refresh while still learning a new concept. How ingenious...

[@amggaming3528]

When you're watching this in a panic the morning before a test.

[@meanqueen0024]

amgGaming SAME

[@jacobhorton3091]

lmao before a final

[@josepreciado870]

amgGaming me too 😂😂

[@magakag7639]

It is lazy people like you who are slowing the World

[@ksks0721]

me rn

[@93stormer]

I hate math, usually because I can't grasp the concepts as fast as my professors and teachers wanted. I wish I had found out about this site earlier. Khan does a great job of explaining; way better than staring at a textbook for three hours at a time.

[@vishvakseenichamy]

Ah windows 98, we meet again

[@huzi__]

​@@sumedhkureel3030 This video was made in 2007, what are you on about?

[@smirk6154]

@Huzi yaa moreover that ain't a low quality vid .it's just simple.

[@awsrhaimeh911]

this guy is a math genius

[@Phosphoer]

Just got back from math class, watched this, and now I understand limits :p Great work :)

[@aneisam556]

this was very helpful, for my upcoming exam on tuesday

[@binoyjohn1113]

who else is binge watching this?

[@arielvinda6624]

Here! 5a.m., working on something, bingewatchin it as noise in the background

[@binoyjohn1113]

nicee

[@anoushkatabachnikoff3890]

all the other psychopaths watching math for fun

[@lauriannek192]

Anoushka Tabachnikoff 😂😂😂😂

[@theChristianChristian]

You literally saved me from a loss of emotional damage. I may just pass. THANK YOU!

[@MominKhan-jk9pu]

Lol. Did you pass?

[@shubhmittal1189]

Sir you are doing great job You are giving the people their birthright to education for free

[@DrCureAging]

Wow. 1600+ videos all by yourself. You're a living legend! You're not boring like those math teachers in school.

[@Alarm451]

This guy is very clear, I don't understand how some ppl can't understand this.

[@AndySaenz]

No, I worked in the Avionics Engineering dept at US Airways. And before that, I did some research using MATLAB. I've taken math classes well beyond calculus, into partial differential equations. I got a B in PDE's, but it was still a very hard class! And I know and understand that math is very useful in the design process, but I still haven't used it in my work yet.

[@disgracedmilo]

Have you used it yet?

[@GGAlice1]

well im finishing up my semester of calculus and this is what we started with, now textbook to textbook what you learn is in different orders depending on well what the writers feel is a good order. according to their websites the calculus playlist does follow my last 18 weeks of study. with minor variation that you will get like i said from class to class.

[@leannemelton1643]

KHAAAAAAAAAAAAAAAAAAAN!!!!!! You're awesome! :) I think I'm going to actually pass my Math 110 class now. :D

[@olesyaliman2209]

I was born the year this video was made, now it helps me get through my math classes

[@devanshadhikari9085]

Khan academy is a life safer

[@リチャ-i3f]

I graduated 3 years ago and already forgot about all of this... (going through my old liked videos)

[@coppee4324]

In 10th grade rn, my teacher made us watch a video for this on college board(ap pre calc) I didn’t understand it at all and she didn’t rlly go over it in class, this helped sm

[@vanchark]

If I weren't taking the class for the extra grade point, I would just go here all day and I'd be ready for the AP test.

[@vasukumar5727]

and now it has became a great platform.❤️❤️❤️🔥🔥🔥

[@adda180188]

oooh ur so patient. and i think u have a very soothing voice. thanx!!!!

[@DMomsFan1]

this was uploaded 7 years ago!! hence the laggy computer hhaha

[@GuineaPigWWE]

going from a recent video to an old video is such a funny experience!

[@HelenWang_zf]

GuineaPigWWE definitely loll

[@jhoshyhyacinthe2880]

gymnastdancerstuff Eleven?

[@plongplongjusainramira6795]

@@jhoshyhyacinthe2880 12 years ago lol

[@IndraD]

12 years now OwO

[@bcnicholas123]

who's watching to get ready for college

[@daelmondejar8536]

I'm watching to get through college.

[@blader20297]

+Jarm Harleyk yup

[@insanarafat8832]

I'm watching it just to make sure I'll not sit in the xam hall empty headed.

[@uwcuberreviewsunboxingsand3711]

Brendan Nicholas Getting ready for middle school...

[@natehoffmaster6726]

UXCuber Reviews, Unboxings, and More Another Cuber! Yay.

[@fedyonok456]

even 16 years later , you helped me with limits ! thx

[@Tungstenum666]

Ahhh! nothing like a good dose of math to soothe the brain!

[@experiencebg]

I completely agree with you, the hd videos look so much better.

[@scottycatman]

@leeko518 99% correct. You just have to remember that z can be a function of x, so you can't say f(x) and y are synonymous. Everything else you said is solid!

[@nerduto1]

Thanks for the video, Sal! It was entertaining!

[@fefafe334]

thanks for mking this as understandable and as easy as possible..

[@parsasamandi569]

Simple, understandable, this is what I want! Best wishes

[@satyamkushwaha3723]

Now its been 12 years. Following you since last 2014

[@ssamerica3062]

I never thought I would find calculus so thrilling until khan academy left me on a cliff hanger.

[@mikem4481]

right. lol

[@laneadamj]

Khan Academy is the best!

[@NoelJustin-hq1mv]

The ending gives a lesson that prepare early for your test not the morning of the test day

[@noueruz-zaman7894]

For my masters program, I am using Khan academy to study economic, maths, statistics, econometrics and a bit for accounting, so at the end of my course i could technically say i have passed from Khan academy!

[@slapointe31]

Wow, thanks a lot. I'm back in school and math are so far in my mind. Looking at your videos help me a lot for understanding. My teacher actually get through this too fast for me. Thanks again. (excuse my english but I'm a french speaker)

[@smitrib]

Sal's basically the reason why half of America's high schoolers can pass their college entrance exams. We love you!

[@Walphyy]

wow this gives me hope to not miserably fail my test tomorrow!

[@AndySaenz]

Well, that's just your own opinion. Because when I worked at US Airways, none of those engineers ever used any calculus. But yes, when I designed a rocket in my rocket-propulsion class, all I did was integrals, limits, etc., to calculate mass-propellant ratios, trajectories, etc. And now that I'm taking environmental prediction, I'm dealing with a lot of PDE's.

[@renewd]

Since f(x) = (2x+2)/(x+2) is a constant function [f(x) = 2], except at x = -1, the y values are not approaching 2 as x gets closer to -1, they are exactly 2. This makes sense because 2x+2 factors to 2(x+2).

[@ehatipo4598]

Doing integral course right now but back in here because your teachers couldn't teach you what a limit is.

[@Goproflying]

"somethings wrong with my tool" May I suggest a Urologist?

[@indraneil8469]

Damm, a 14 year old video helping me now in 2021

[@sansamman4619]

I can't believe you had bad computers I love you sal

[@wenhanzhou5826]

You definitely deserves some better techs

[@shubhamshinde5458]

It help me alot

[@clarinetmeister]

For f(x) = 1/x, the limit as x approaches 0 is negative infinity from the left side and positive infinity from the right side.

[@farzero]

thanks a bunch man, these videos are amazing. I just got out of class and I've been watching these videos for the past hour, very helpful and entertaining.

[@brajeshmohanty2558]

Those who found this video after 2021 be like wow I found a treasure ❤️😘. But still I am watching a night before my midsem huehue 😂🤣🙏

[@TolisFrag]

Well,it's a fact that it can be done with more than two ways!I don't mean to correct none,I'm just saying! Since 2x+2 it's Differentiable and x+1 is too.So by the Del'Hospital rule you can find the derivatives and you will have lim(x->-1) 2/1 = 2 It's the most easy and fast way finding limits,when you can actually use it. Here in Greece,we have done all limits as well as we have laernt ho to use the Del'Hospital rule ,before we become 18(the last grade of high school)

[@sidstam]

The limit is 2, but the function is undefined at x=-1. See his last video in which he shows the difference between the value of a limit and the value of a function when the function takes on an unexpected value; I believe the example he chose was f(x) = x^2, f(2)=3, so lim x->2 of f(2)=4 (despite f(2) being defined as 3 for the function.)

[@momeika]

oh god i have a test tomorow and this is like my last resort...this is not how i planned my senior year in HS and we cant even use calculators...and i do get the concept its just that our teacher is really big into labeling and sometime like if we dont label the right things we get points taken of and that really hursts the grade...

[@jackjiang7535]

You are explaining it so well. Thx a lot!

[@abunigel13]

it all makes sense!!!

[@liyabrown2206]

I am so happy I made it to 6th grade thanks allot Khan Academy

[@Runningscared4ever]

For The Win!!!

[@braining1]

I swear that if I had the money I would give a millions computers so just keep going and thanks

[@The_One1]

I find these videos extremely helpful

[@mrhnm]

You can I used it and went out of remedial math 0750 (around middle school math) and into intermidiate college algebra.

[@synchronium24]

@jiffy973 Sort of: the limit from the left is negative infinity and the limit from the right is positive infinity. However, customarily, it would just be positive infinity because people tend to refer to the graph of the function for x>0

[@MSA_madi]

Thank you very much bro, God bless ya~ ^_^ first time got interested cuz now I know there's a sense of people invented this headache math problems.

[@jayshreebalaganesh]

who else is watching it in 2k18?

[@B6Videos]

The best 240p video ever

[@WilliamLadu-wr4bb]

Very interesting.

[@namanjaincool12]

best teacher

[@oOdorieOo]

from now on, I won't even go to lectures at my university, I'll just ask for the list of the topics we're supposed to learn in the semester, and search the videos for them on this channel. :))

[@MsGrammarnazi]

You have a really great teaching voice. Oh! I like the lime green pen. Dana

[@DarkKiss92]

you make math really simple, clear and interesting! Thank you very much!:)

[@schirantube]

Understood !! Thanks

[@GGAlice1]

it was very confusing for me when introduced also, but your not always solving for a y value so using f(x) early on helps the transition when your not solving for a y value (x,y) as a point = ( x, f(x) ) it just means what is the result of x pluged into the function basically function(x) = some value. hope that helps.

[@thechessgeek]

I LOVE MATHH

[@jessicareed3417]

I'm watching this and I'm not even taking calculus

[@ankitaaarya]

it just means youres curious and wanna try learning anything, even you cant understand it. theres no prob. people should be like you

[@Tanner_29]

Same here I’m in 7th grade and I’m learning this just to learn it

[@nellajayec]

i love the part when he says" undefined, uuuundeeefinneed" in a low voice. XD 3:45

[@hoseinqadam]

Hmmm but it is still useful when it comes to finding velocity of rockets and charting a course for satellite, my friend's dad is some kind of engineer (not sure what kind) and he said that his dad uses calculus nearly everyday, maybe it is the field of engineering a person is in.

[@GTSRBOY]

good old windows computer breaking down anyway nice tutorial your the man

[@aoshappyworld4264]

Great explanations!!!!

[@rutee6967]

clear explanation

[@subhradeep34517]

Nice it's way too good

[@priyamathematics3953]

What a great day ❤️ ...

[@mike65535]

It's more realistic with the stumbles!

[@mannelijkheid]

right before 2:50 you say that 2x+1 over x+1 is the same as 2(x+1) over x+1 and then you cancel out the x+1's and that it results into 2. But isn't the bottom part the same as 1(x+1) which will leave you with 2 over 1 after you cancel out the x+1's?

[@32docholiday]

HAHAH - ur a funny guy - compter froze , really appreciate ur videos, *start easy then get into harder problems - like the limit of a sin, tan or cos function(if u can). thanks a lot!

[@catcroissant7700]

Why am i even watching this ? I'm from the UK we don't do calculus. Oh well there's 200 videos here and I'm oddly hooked

[@colinchambers4760]

Thank u so much i LOVE U

[@richardoctovianusoey]

yeah you guys can turn on youtube captions too

[@sreejachakraborty6145]

this is just AMAZING!!!

[@allymwashambwa5920]

I really enjoy the periods

[@lorenzosan18]

thank you :)

[@sosilly3008]

here 12 years later. its 2019. time flies

[@shrutijain1998]

Me too from 2019!!

[@redranger545]

undefined, undefined, undefineeeed

[@janicknorman9396]

classic 2007 video lol

[@MunchVids]

You could say y=f(x) and then use y.

[@jiffy973]

plus or minus infinity right? is the answer to the last one

[@marathonpro92]

1 million views means panic. WE'RE ALL GONNA DIE!!!!!!

[@smolboyi]

maybe one of these days I can be smart like you Sal