Calculus: Proof of a limit

[QuinceyFoxx]

John Cena gets mad at calculus.

[hubomba]

This guy> Thomas Finney.

[gibilaro]

def is a mathmatical version of dexter

[louis424]

but a thousand thanks for this video

[louis424]

you remind me of Dexter for some reason

[Justin0124]

Professor went over this today, and had no idea what was going on. Understand now a lot better. Question..is the aside work you trying to get a conversion factor for how the x values are changing compared to the y's? The slope is 3/1 for 3x-30 so the x values would me moving 1/3 as many units as the y's. is (1epsilon/3) any relation to that?

[natash179]

I lovee youuu

[HardkoreRocker]

at 12:47 i went like HOLY SHITTTT how well this guy explains things. now calculus might start gettting a little more exciting, professors nowadays suck!

[giantfan779]

you just saved my gpa

thank you so much

[giantfan779]

you just saved my gpa

thank you so much

[St3v3n947]

everything you said in the beginning is so true..

thanks alot i wish my teacher was at least half as good as you

[nellycorture]

Thank you very much for this, it really helps :)

[gregg4]

"Can you think of a more obscure way of saying anything?"

LOL!

Gregg

[JahRo225]

This is by far the most understandable, explanatory video on the subject of precise limit definitions. Thank you so much.

[mikeberryman27]

Awesome explanation!! Thank you soooo much!!!!!!!!!!!

[BangingBox]

WOW Thank You for the great explanation !!!

[gamezboi8409543]

6:15 to 6:24 i never knew this was a comedy. funniest part right here xD

[AmirasCareless]

I dont usually comment videos, but you are really great teacher, you do consider your time wasted by making videos and explaining to people. Would be great if we would have more people like you. Respect.

[orgasplosion]

You are awesome

[bkhan79]

thanks sir.it was realy helpfull.our caculus teacher is realy a dustbin.thank you once again

[RanmaRanmaRanma]

thank you for this

[ImalHasan]

Calculus is quackery for sure.lol The Eygptians and the Babylonians aka THE SONS OF HAM, already gave the world Algebra. 3000 years later the world in 2010 still uses Algebra to solve problems. Algebra is easy to learn and use. Calculus, lol, what a joke. Who in the hell even knows what this guy is talking about. I dont even think he knows what he is talking about.

[BenU314159]

@ImalHasan

Are you fucking serious dude? You realize that without calculus you wouldn't be watching videos on a computer right now right?

But converting videos into digital images and transporting them through fiberoptic cables and satalittes using calculus based transformations are all jokes too right?

[ImalHasan]

@BenU314159

1st- the computers we are using right now are based on the binary system of 0 = off and 1= on Bro. This has nothing to do with calculus.

2nd- please tell me what calculus technique is used for converting and transporting video images through fiberoptic cables

[jordanbaker424]

@ImalHasan

Electrical engineers use calculus to determine the current needed to get the signal over a specific distance without it all being lost (lines are curved because of gravity, calculus problem right there). If it doesn't add up, the lights (or the computers) don't turn on.

Also, there's actually a field of engineering and applied science who's main purpose is the design and application of optical fibers, known as fiber optics. (wikipedia). 

[usurper17]

Wow. I would gladly have paid $500 extra to take calc with you instead of my whack professor.

[LilDude4rmdstreet]

yea, i understood it but i still need a little more help

[kippyjohnson]

You sir, have made my day. This is the best video on youtube, hands down.

[lostguy4815162342108]

thank you, sir. very much appreciated

[MyDogBrownie]

he cleared it up a little bit.But he's throwing me off with that Epsolon and the Delta

[icyunvme95]

This was a tremendous help, thank you for putting this on youtube. I will definitely come back to your work if more help is needed. :-)

[michaeljbergin]

Compliments from an old man, watched most YouTube content on limits, this is the simplest, most direct explanation I've found. Thanks for posting.

[corbinflow]

I DIDNT KNOW JOHN TRAVOLTA IS A MATH AIMBOT.

[slipinslidebob]

This man is a.....GENIUS!!!

[ohhgeeme]

finally understood the whole concept behind limits.

thanks a lot. you explained it way better than my textbook and my professor.

[allisclothzoff]

THANK YOU!

[silentc1015]

Thanks a lot for the video. It was very helpful!

[DigitalCatalyst]

This was fantastic. It simultaneously helped me understand limits better, and made me feel better about taking Calculus, which given that limits were my first exposure, was looking pretty dull and not at all as fun as precalculus had been. Thank you!

[spinynorman1982]

Thank you for explaining this so clearly Joe from Family Guy!

[nunoadiga]

So greattttt ! i liked it very much

[funnyj]

can you do limits of multivariable equations. like f(x,y) using the epsilon delta proof. I know how to prove that the limit does not exist but im so confused on proving IT DOES. please and thanks

[funnyj]

so easy, even a caveman can do it

[Boris0000]

Thank you very much !

[kerrymiller4]

I loved the explanation easier to understand now.

[savysosa]

Thanks this was well said

[chrisrave]

Yeah, I agree. I liked his choice of words when he referred to the relationship between epsilon and delta as, "aspect ratio."

[sano0311]

You should make more videos, because people like you keep me going to school.

[Hohn89]

thank you very much. I took Calculus my second semester of college and dropped the second day of it.. I love math and the way my professor started up freaked me out.. I felt like I had no chance.. I've gotten back in with a different professor now, my third semester, and seeing this video, among others, have really helped me to understand what's going on. With all small arguments like 'meat of calculus' kid under me aside.. you helped me.

[MarioTutorials]

you look like a guy from a serie I see on FOX.

[Archer6633]

@MarioTutorials 

What seris?

[MarioTutorials]

I don't remember the name, but I think it was an FBI agent that had some kind of powers. I don't see it that much.

[Emilyelizabeth23]

Very helpful! Thanks.

[Arycke]

Hold up buddy, it has much to do with the "meat" of calculus. If these students got turned off, they shouldn't have taken calculus to begin with. The limit is really a notion that is within all of calculus, especially when you move on from the easy notions of basica calculus to Analysis and measures. It's part of the fundamentals of calculus. Ignoring it is almost like ignoring addition. I'd like to see you integrate a function (non-numerically) without the existance of limits :) Cheers.

[TutorWizard]

7:25 can you think of a more obscure way to say anything haha

[ratanraj1412]

you are angel ... thnx

[speedynine]

great video. don't know why most teachers can't explain like you.

[wirito]

kindly, piss off ROFL.

[JPraise100]

thanks

[clixsyt]

You explained it so well.

[hpsfl]

That breathing creeps me out

[1Mperios]

If you can just think about the breathing then I guess this video isn't for you. Please kindly piss off.

[Sk82beast]

yea

[wzerl]

Eres una verga!!!

[wzerl]

Eres una verga!!!

[MTSCNATT]

This guy is great. Very clear when talking

[lost123]

Thank you, bro. You were the only one who could help me. Videos like this should be used instead of the useless textbooks.

[tino8554]

It's called class buddy

[MisledTrick]

@lost123 So true. FUCK SPIVAK's CALCULUS!!

[deltaklm]

wow, thank you so much! I've been reading my book/examples for the past 2 days and was lost until I saw this video. I think you just saved me my quiz grade.

[childworshipsbuddha]

Videos like this are the reason i love youtube. thank you!!!!!! this video is extremely helpful.

[nexttoradio]

good explenation of a limit, even though i already understood that from last year. So i agree that learning this first is like shooting yourself in the foot. Above all i needed to learn how to do a proof, since my teacher decided to come back and do it this year. I just didn;' get it but this helped alot. thanks!

[postalass]

Thank you for explaining. And you are right when you say that it turns students away. I couldnt grasp the reasoning behind limits and didnt understand the point of it. It all seemed like substitution of the "x" value with the approaching number. Thanks a lot. I wish you were my professor

[zilvercederbom]

Many, many thanks. =D

[rkazarin]

Thank you Sir

[masterchief377]

Thank you so much

[NateDawg80126]

Taking this class in college now and after 2 days of class, I still have heard no simple explanation of the purpose of the class.  This is exactly what I needed, why more teachers don't break it down like this is beyond me. Especially as a visual learner, this is really important to me.

[joneschri6]

thanx alot this really helps = D

[clarkindee]

I've watched this twice and i think I finally understand this. "If this did not happen, there there would be no limit." LOL. Thanks for your generosity in doing this.

[onegirlincali]

could post the solution to the integral (indefinate) of

v arcsin v dv

Please and thank you in advance!!!

[KaiChippi]

you;re awesome

[solo2wolf]

Thank you very much for sharing this. Beautiful stuff.

[TheSkinnySpencer]

Appreciate it!

[cycro27]

Thank you SO much!!!!! This finally makes sense! Btw, love your little smiles before and after cuts:P

[jdbrown371]

I agree. Calculus without limits simply isn't calculus. The only real calculus books I've ever found are Spivak, Apostol, Courant and Landau. Another subject which is absolutely massacred in schools is linear algebra.

[Hy22n]

great thanks! It helped me to understand it better.

[kikosolo360]

gringo marik te volaste la ultima parte, PANGA!!!

[ohmannhey]

Thank you dude ...

[M0L0T0V4]

thanks so much brotherr

[beatonbros]

Thanks. You're awesome.

[EmperorCesar]

Great stuff

[CR2380]

you're a wonderful teacher; thank you so much for taking the time out to do this. you've helped so much!

[Cipher1337]

great video maybe you could show some infinite limit proofs as well

[scott5878]

thanks for the great video!!! ugh i really needed the help ha ha

[greatkiller]

I love this cat. "Can you think of a more obscure way to say anything?" LOL! Sounds like Troy McClure

[younesb91]

The distance is (a-x) :)

[lagrangemultipliers]

he meant absolute valu of x-a it gives the same answer if u plug in numbers.

[sjsawyer]

lol 360 mph.. good thing he didnt stick with 5 miles.

[Ruudboy419]

big up.You made my day.Ruudboy 4rm uoit...

[klondikebar2]

haha, you can see him turning his head to telk to the camera, even when hes of-screen.

nice vid tho

[DeCooliePrincess]

you made me understand the true meaning of calc. I hated it and thought it was useless to now. Now i have a whole new veiw for when i go to class.

[RubberDuckyToy]

LOL! I love it when you said: Delta a Greek Letter,... Epsilon, again another Greek Letter,... Can you think of a more obscure way to say anything?

I have to wholeheartedly agree with you. The way they explain the concept of limit is so obscure that it was a big turn off when I first saw it. And it's still is had you not explained it so eloquently.

[shim2dawg]

great video. thanks!

bottom of the final proof is cut off.

[PiotrTarasov]

It helped me so DAMN MUCH!!!!! THANKS A LOT!

[mu24evr]

Excellent. Thanks!

[pr0metha]

Really,really nice explanation. If only my teacher was so good.:) I owe you one!

[lucabrazi6]

5 stars

thank you so much

your now my new math teacher

[kingjoker54]

18 what the hell wrong im only 16

[ibreakkidslegs]

im doing analysis in first year university and the limit proofs theyre hitting us with on the first day of limits are outrageous. they dont teach you anything about what you're allowed/not allowed to do when proving, which makes it that much more impossible

[friendlyfire53]

great. thank you

[dancinmit]

Thank you so much for these videos!!!

[diabloman91]

Wow!

TYTYTYTYTYTY

You have made it so much easier to understand. =]

99*/5*

[kissyoko]

great teaching!

[bezzer1185]

its John Travolta! thanx

[mgmoeab]

lol. I just noticed.

[jarardio126]

Wow. That was excellent tutoring. You explained it so much better than my teacher did. Thanks!

[alinjohn1960]

nice thank you sir, thanks alooott... are you professor of any college or university ?? we want calculus teacher like youu....

[Nanumir]

thankz midnight tutor

[altcmdesc]

Most AP Calculus courses do not cover the Epsilon-Delta definition of a limit...

[MissBee77]

nice explanation of something that seems "completely off the wall"

:) Thanks a lot!

[subwaybusker]

thank you thank you thank you! you have been a great help especially when the majority of rofessors and textbooks are of no use. thanks again! =)

[matrixate]

You know, I tutor students in Calculus and I really enjoyed this professor's explanation and attitude. He exploits what most instructors are afraid to say in a classroom. A+

[elganch]

gangsta, i like the shrinking box analogy.

[terranark]

holy newton!

this blew my mind dude,something raw just clicked in my head,i mean i get B's for university calculus,i didnt really take time to really evaluate why calculus is there,i mean i figured,hey its on my course so im going to do it,but now that i think about it.wow,you actually do this stuff everyday without realising it,a lot of situations in your life cant be determined by instances.that x->a but is your instant,the F(x) is your path,the limit is the particular

[nuktu]

snore....

[payasitopimpim2002]

awesome teaching....thanks from lima peru

[ronaldfdoculan04]

ahhhhh.

soo desu.

i remember doing this thing!

hahhaha

[EzeffinE]

why don't you just simply state that you are trying to find the instantaneous rate of change and a select time or x value? Calculus is after all about rates of change

[adda180188]

thank u !!!

[bernardrb36]

I watched the explanation three times, and finally was able to track the proof.

The thing that hung me up was the subtracting of the greater value from the lesser to determine the sizes of delta and epsilon. I am used to subtracting lesser from greater values in daily life. Even NASA does that in its countdowns. Can we do this proof using a - x and f(a) - f(x). Wouldn't that be more logical?

Why is the mental twise necessary? I'm sure this instructor isn't trying to confuse. Nice guy.

[mtheoryx83]

Ah, now it's all making sense.

[cjpaco]

very good

[dakamalu]

In fact, I think the whole definition is poor. I agree with squeezing the epsilon neighborhood arbitrarily (because that forces approach to the limit), but the definition MUST declare also that the delta neighborhood is actually getting smaller!!!! Not just that it exists!!!!!

[cjpaco]

buen profe wey. Saludos desde mexico

[dakamalu]

I don't agree with this. The definition of a limit forces the epsilon neighborhood to approach the limit, NOT the delta neighorhood.

[baroqueoboez]

What about in rational functions when f(x)=(x+1)/2x? I know it approaches a horizontal asymptote of e, but is that the limit? Is a horizontal asymptote the same thing as a limit?

[kickwear]

Actually if you came closer to (a) and f(x) increased, it means the limit would be infinity(+ or -) the only time there is no limit is when you approach (a)from the (-) and then approach (a) from the (-) and the numbers come out different is when you don't have a limit.

[midnighttutor]

Don't see how you can call infinity a "limit" since it is inherently unlimited but I get your point.

[kickwear]

the fact that it is a limit is because it's not all numbers, it goes from a certain point to positive infinity. if it was just infinity, meaning that it goes both negative and positive infinity it wouldn't be a limit. But negative infinity or positive infinity can be a limit. Just not at the same time. Maybe that helps?

[papipoto]

THANK YOU.

[453hbhk4]

please say your not a teacher,you know what yur talking but you can't explain it! btw i have a dagree in mathmatics and love the subject!

[oOCheloniaOo]

enjoy your 'dagree'

[MelissaS6588]

Your explanations help me a lot when I was working on my online History of Math course. We needed to explain the epsilon-delta method and then create an example and I was able to do this after watching your video. Thanks!!

[pgzero78]

Fantastic... keep up with these videos...  that way i can pass..

[drewday]

"I don't even know to what extent analogue speedometers exist anymore."

What kind of car have you been driving?

[blackberryjuice1]

teaching doesn't pay, he does this out of the kindness of his heart.

[drewday]

My comment wasn't meant to be an attack - just an observation of the fact that few cars today have digital readout speedometers.

[zati10]

good explaination, i spent like 2 hours trying to figure what the fuck epsilon and small delta are doing

[corona7w]

You seem really nervous. But good job, now I will not fail my finals.

[vuxfeon]

i wondered what happened to roger ramjet after his show got canned.

[vuxfeon]

i take that comment back. this guy is a good teacher, wish I had one like that back in the day.loved the "can you think of a more obscure way to say anything"

[theologian27]

I´ll Be very honest.. U a great tutor.. Awesome.. love the vids.

[FarFromEquilibrium]

Thanks immeasurably! this rocks XD

[stevnricke]

i love you

[herzogsbuick]

Brilliant, thank you

[77gregory77]

Great vid. I've studied and taught math for years. Thanks for the "aside" and and the practical explanation. It's perhaps the clearest and simplest explanation of the Proof of a Limit I have witnessed. You served it up on a silver platter.

[johntkucz]

instant=fleeting. nice. very human explanation grounded in great examples. This clarified MANY calculus concepts i've been trying to understand. Are you a math teacher? I love how you almost ridicule it at the beginning, "why even use this?" etc. great stuff

[fluganSWE]

great explanation

Keep up the good work!

[1994camaroz28]

Nice work.

[brokenFlask]

wow

[Zevcollins]

Hah, seems the American education system is just as bad as the Australian one if something as integral (lol) to the world as Calculas isn't treated with the proper sensetivity.

I remember having to figure this all out for myself back when I first did it. Calculas is still by far my absolute favourite Mathematical tool.

[mojib]

thank you for teaching us the very important problems in mathamatics

[dontstealmybike]

Hi Midnight Tutor!

This video helped me immensely towards understanding what a limit actually is. I completely agree with you that one of the flaws of the AP Calculus course is that they begin with such an obscure topic. Thanks for your help and keep up the good work!

[alfwiz]

Thanks Sir,

I have always struggled in math. I really enjoy your videos.....keep them coming!

Sgt Alford

US Air Force