Limits of Multivariable Functions - Calculus 3

[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/

[@johnch2800]

Khan Academy gets constantly so much praise and they deserve it, but for someone looking to pass with 5 days of studying in the whole semester videos like this are what truly can help.

[@PunmasterSTP]

How’d the rest of your class go?

[@mrbanana6464]

This guy is good for learning how to do something quickly, but for more rigorous math you’ll have to stick to a textbook or khan academy.

[@dudeiknowman]

@@mrbanana6464 accurate! Like the parameterization at the end? Lost me.

[@tiangong6616]

I think it depends on what you are doing, for math major this is not enough, but for engineering studies, this is very helpful

[@janeh9962]

0:00 direct substitution 0:43 manipulating equation to allow direct substitution 1:53 proving the limit D.N.E. 4:15 proving the limit D.N.E. 6:59 direct substitution 7:35 proving the limit D.N.E. 12:40 manipulating equation to allow direct substitution 15:20 using parametric curves

[@isi6402]

Thanks

[@PunmasterSTP]

Thank you for the timestamps!

[@batuskovichuman6886]

you are angel something thanks

[@kimjongtrill2399]

Just came here to say I've watched all your Calc videos, don't know what I'd do without you. I'm on Calc 3 now so keep em coming!

[@AlonebutUnstoppable]

right

[@scottwillard7998]

Same here, he made Calc II a breeze. Calc 3 is harder though :p

[@scottwillard7998]

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[@shibozhang3787]

@@anirudhbukka5413 Mathematics courses are both in science and commerce program. Some concepts are same between science and commerce program, only the applications parts are different

[@dontreadmyusername6787]

Are you huys seriously self-teaching calculus???? I mean college courses are hard enough

[@lidyasolomon5557]

Lmao pray for me...I havent paid attention all semester, but my final is tomorrow. I'm cramming with his videos. hahaha. This could be the first class I fail in my life. Jesus take the wheelll. I got an A in both Calc 1 and 2 so if I fail it would be a major disgrace for me and my GPA. I'm on the honors list, so hahaha pray for me.

[@lidyasolomon5557]

Euchariah Brown got a 78 and ended the class with a B

[@lidyasolomon5557]

@@ampleeeeeeeee thanks lololol

[@PunmasterSTP]

@@lidyasolomon5557 Awesome; I’m glad you could pull it out! 👍

[@lidyasolomon5557]

@@PunmasterSTP lmao thanks I graduate with honors we good 😭 how r u

[@PunmasterSTP]

@@lidyasolomon5557 That’s excellent to hear! I’m doing fine myself.

[@uke4382]

You are single handedly giving me my math credits towards my degree 😂

[@radityafajri9009]

I think in the last example, when we approach the function from the y-axis (which gives us x = 0 and y = 0), the result doesn't equal to zero. So, from that, we can conclude that the limit DNE.

[@付相龙-b2t]

yeah, for the y-axis I got 1/2

[@jacobcherian4699]

@@付相龙-b2t yes same

[@noorbashashaik6998]

Yeah that's right 👍

[@noorbashashaik6998]

There itself we can say that limit doesn't exist

[@alexthred2179]

So glad I'm not the only one who saw that, I was freaking out thinking I did it wrong instead of him just using the equation to teach using parametric curves.

[@samiabdullah6902]

16:43 last example the y -axis when z=0 and x=0 its equal 1over2 which not zero

[@ahilanarivarasu5887]

Yea bro. So we can conclude that limit does not exist at that step

[@pranavbhanot816]

Yea I did the same too

[@pranavbhanot816]

But he is trying to teach us more ways to solve incase this one didn't work in some other cases

[@ahilanarivarasu5887]

@@pranavbhanot816 yep

[@M971-o5g]

You’re right

[@gautamkalra1325]

best channel for engineering maths studies istg Idk what I would've done without you

[@JN-jx7nx]

i love it when a topic I'm struggling on has been explained by ur channel-- else cramming for one night would've been a nightmare

[@nikhilavishek359]

I always wonder, why the channel name is The Organic Chemistry Tutor when a person who is teaching is actually a gem in mathematics.

[@quamos99]

You are the reason why am still surviving calculus

[@jeenagurungfuenjnsvuc2769]

If only i had a maths teacher like you before.. I won't t have been here today watching your videos. But I am glad that i watched it. You explained my whole degree in just these minutes. Thank you so much. 💛 Your videos are worth watching...

[@akshatsrivastava4280]

Which degree are you doing that can be explained in a basic multivariate calculus tutorial video

[@RaqimKeitheile]

@@akshatsrivastava4280

[@SonGoku-wd4mi]

Calc 3? im so far gone from calc 1 trying to find an answer from a test... good luck Uni students doing this.

[@vinniesanchez9824]

I’m in Algebra 2 as a sophomore and I understand this. That’s how good this guy is at explaining math.

[@AlonebutUnstoppable]

right

[@SunSunSunn]

Wtf. We finished Calc AB as a sophomore lol

[@lidyasolomon5557]

tbh calculus 3 isn't that hard....try taking Differential Equations ...Undergrad classes aren't that bad tbh. It's those Master's level classes that are insane.

[@moatef1886]

@@lidyasolomon5557 Actually, calc 3 is straight forward in the fact that you kind of already built up the foundational skills in Calc 1. Conceptually though, calc 3 actually gets really hard you just don't get tested on some of the topics that can have problems that get really hard (and are applicable to areas like engineering, physics etc.). You barely scratch the surface of partial differentials in that entire chapter.

[@debasishkundu7830]

This is absolutely amazing!!!!!!!!!!!!! Why don't we have teachers like you in school????? 😭😭😭😭 life would've gotten much easier!!!!! 🥺

[@shae7153]

All smiles right now. Thanks for saving a soul

[@scottwitoff8932]

Is there a limit as to how many topics you can cover? Keep up the good work!

[@hankhudson8736]

The limit approaches infinity

[@mikuculus3720]

It DNE

[@Algebrainiac]

Okay…… I mean I do understand what he’s talking about here… however… usually they decide to do the limit as (x,y)-> (x,0) and not the limit as x->0 because then we’d have to remember that if it is as x approaches 0, we must not do direct substitution for x=0… I hope this makes sense. At least to him… idk if anyone knows what I mean but that’s why it confused me when I was learning this… but other than that this is great!

[@bjornvanderlande7491]

really good video thanks, just had a question. In the last example you stated that this problem couldnt be solved by travelling over a certain axis, but if we travel over the y axis this limit becomes y^2/2y^2 which is 1/2 which is different than going over the x or z axis so the limit doesnt exist. Or am I overlooking something?

[@AlonebutUnstoppable]

right

[@Onlineshoppingcomparison]

Yes I got the same too

[@hannanbaig7888]

@bjorn van der lande Same happened with me. I came to the comments section when I got y^2/2y^2 which is 1/2

[@gold9994]

It does not exist. If it fails to be the same from whenever we approaches, it's not existent.

[@jackpokrywka542]

@@gold9994 yea that’s not the point, he made us do an extra few minutes of work just to figure out what we coulda gotten if we used x=0 and z=0. I mean it was useful learning the substitution with T but he still shoulda used a different example equation tho

[@Max-cu6bw]

Just a question, for the last problem, approaching from the y-axis, leaving x=0 and z=0 wouldn't you get 1/2 which also proves the limit DNE?

[@nivekonthebea7477]

i got the same question

[@weekendfriday22]

i did thge same thing

[@sujay.b1517]

16:32 approaching by y axis wont give you 0 but 1/2 .

[@Cocaine_officer]

can anyone explain in 16:35 along y-axis we have x=0,z=0 don't we get a limit of 1/2

[@satishshinde6420]

Thank you sir one video solved my all problems

[@mentor_172_adriansyahariak7]

16:36, I'm sorry but if I check with lim y->0 which is (x=z=0), i got 1/2, isn't it?

[@usaball9193]

ya, I got that too. In that case the limit doesn't exist

[@mxgvn]

The last example helped me on my quiz so much for proofs!! thank you!!

[@ValentineChinedum-zk9up]

Organic chemistry tutor! SAVING STUDENT'S GRADES TILL ETERNITY🎉

[@georgesadler7830]

Professor Organic Chemistry Tutor, thank you for solving Limits of Multivariable Functions in Calculus Three/ Multivariable Calculus. In some cases, Polar Coordinates can also be used to evaluate Limits of Multivariable Functions in Multivariable Calculus. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

[@이승재-z8s]

question about the last problem, is it okay to let x,z=0 and the value becomes y^2/2y^2 which keeps value 1/2 and can say it's limit dne?

[@khbye2411]

Your videos are fast and to the point! Thank you I'm not even a chemistry major hahaha

[@evelynnechin9449]

thank you so much. this saves me so much since im a visual learner

[@durgeshjayswal3686]

Good teaching sir I am indian

[@yamatanoorochi3149]

12:36 then I have to also think of a relation between y and x that'll make me find a way that the limit doesn't exist, and if I can't think of one even though there is, and all the previous steps have the same results, then I'm getting a wrong answer?

[@upaldebnath3812]

THIS VIDEO IS A LIFE SAVER ,THANK U SO MUCH

[@tobiashermans5595]

for the last one, just put in 2√y for x and you'll see taking this results in the limit being four, saves you a lot of work. But very good video, keep up the hard work :)

[@kin_1997]

6:59 is that a limit or not now ?

[@hussaini24]

Kudus to d create tutor on KZbin. I'm at d top of my class with d help of ur tutorials. Now in lvl3 & I'm missing ur tutorials on d courses I'm taking. But thanks so much for ur support sir.

[@JF17thunder485]

My professors must need to take your lectures

[@campeoncampeon4520]

46. Limit of a function of a variable. Suppose a function of a variable is given, f(x). Let x take on a sequence of values, nearer and nearer to a fixed value a, in such a way that lim x = a, or x → a in the sense of the preceding section, but in this connection with x = a expressly excluded. With this exception x → a in any manner whatever. As x → a, f(x) will take on a corresponding sequence of values, and it is possible that f(x) will approach some fixed value L as a limit. If so, we write lim x→a f(x) = L This is read "the limit of f(x) as x approaches a is L." (That x ≠ a is to be understood.)

[@ronycb7168]

4:00 The answer is 0 not undefined or 0/0, because we do not care about the value at the point only the value around it, hence shouldn't directly substitute.

[@jainil22_official]

Sir you are very great teacher ☺️❤❤❤❤❤❤❤❤❤

[@zerodegreescelsius]

Watching this to explore if multivar calc would be the right choice for me next sem, given the inadequate support given for Calc 1 by my uni. Now I know who I can turn if I were to encounter problems during the course 👍🏻

[@sruthikolla3231]

U are my saviour

[@ahmetenesacar2326]

Can't we use L'hospital in those kind of questions ? if so how we could determine the answer without approaching value that we are looking for ?

[@memoryanesu]

the best maths tutor

[@riskacendana8085]

i like this type of video. Not too fast and he explained it step-by-step

[@riskacendana8085]

1)subtitusi 2)pemfaktoran 3)cek x=0,y=0,y=x,y²=x (jika salah satu beda maka artinya tidak punya limit 4)kali sekawan 5) dimisalkan dg t (utk fungsi 3var)

[@wetbadger2174]

In the last one when I tried approaching from the y-axis I got 1/2

[@factsheet4930]

Thank you very much! haven't been paying attention in class lately

[@AlonebutUnstoppable]

you are right

[@VuTungLam-pk4sy]

Gosh, your vid always help me, love your work, very simple yet easy to understand 2 hours of my lecture

[@jorgetomaylla5032]

Thank you! I was really stuck in this 3 variable limit at the origin, but this gives me hope to get an answer:)

[@custodioarmindogungulo8465]

This has helped me a lot, mainly it cleared my confusions. Thanks a lot.

[@gehadakrp3607]

if the answer of direct sup. zero over zero it always dne?

[@Liviller]

it might still exist, the video simply doesn't cover it

[@campeoncampeon4520]

A variable approaches a constant as a limit when, after a certain point, the absolute value of the difference between the variable and the constant becomes and remains less than any preassigned positive number however small; and the constant is called the limit of the variable.

[@HNunes-te2zm]

very important point. totally agree.

[@PunmasterSTP]

Multivariable limits? More like “Magnificent learning, and this is lit!” 👍 🔥

[@Australis_]

You are awesome man. Best explanation ever.

[@NASAFanboy]

Love your videos, can you make a Calc 3 final exam review video? Thanks!

[@wassimmani952]

thank you man you helped me a lot

[@harjitkaur4090]

16:23, we can approach via y-axis after trying via x-axis, both answers are coming different.

[@ajz2852]

My professor put one of these questions on my calc 2 final... I had no idea what to do, and when I asked her what I was looking at she just told me to figure it out.

[@edu.islamic]

Sir your lectures are very helpful to me.

[@grantc8523]

This is a good video but I wish there were more examples of 3 variable limits and more problems that are not at the origin

[@empower_andhra]

I don't how to thank u ❤❤ u are just awesome 😊😊😊 omg when my teacher explains any thing I would sleep later I come search for ur video that's it.... U are rockz

[@djslife7082]

Great video, you really blessing the community 💯

[@dianaserra6473]

Hi, Mr. JG. Not sure if you'll read my message.... Being that you posted this video only six months ago, I am truly hoping that you see my post. Pertaining to calculus 1, would you be so kind & amazing and please post a video on limit using delta and epsilon? This has my head spinning right now and I am trying to understand the point of reversing the steps within my work, etc. Please. I would greatly appreciate it. Thank you for all that you've done for this community that supports & follows your page.

[@luisgonzalez-xn8wx]

your great man

[@zarifzaki5781]

Isn’t 3:57 cannot be computed since it is 0/0

[@ghan7241]

no because its 0/y before u even plug in 0, so its gonna be limy-->0 (0) which has no variable so its just 0

[@haritsnasution]

limit to 0 isn't exactly zero but close to 0, it can be 0,00000000000000001 and it's still not 0, therefore it is not actually 0/0 and can be computed

[@terryyoon1856]

I still remember doing this back in my highschool in Canada! Thanks for bringing back my memories!!

[@assaultszn3557]

highschool?

[@terryyoon1856]

@@assaultszn3557 I started studying calculus when I was grade 6 and then i happened to advance through math in HS 🙂

[@metawhirl4609]

@@terryyoon1856 same here I also completed calculus 3 in high school. Doing real analysis and complex manifold theory. I am just here to revise some details

[@farhannoor3935]

don't you guys normally only do Calc.1?

[@aformula4198]

@@metawhirl4609 smart-ass

[@taylorzhou1289]

In the last problem, I think if you set x and z to 0, you will get a limit of 1/2. So that solves the problem already without needing the parametric method.

[@atree1301]

exactly i tried it too and with lim y approaches 0, the result is 1/2 thus proving the limit doesn't exist :)

[@noorbashashaik6998]

Yeah that's correct ☺️

[@noorbashashaik6998]

There itself we can say that limit doesn't exist

[@MyLuisbatista]

at 6:34 aren't the limits approaching from either axis 0/0? I thought that meant the limit DNE, not that its equal to 0

[@tinochigwada4652]

Thank you so much for all your videos. Got me through high school and calculus 2 last semester. Do you have a calculus 3 playlist?

[@campeoncampeon4520]

¶¶46. Limit of a function of a variable. Suppose a function of a variable is given, f(x). Let x take on a sequence of values, nearer and nearer to a fixed value a, in such a way that lim x = a, or x → a in the sense of the preceding section, but in this connection with x = a expressly excluded. With this exception x → a in any manner whatever. As x → a, f(x) will take on a corresponding sequence of values, and it is possible that f(x) will approach some fixed value L as a limit. If so, we write lim x→a f(x) = L This is read "the limit of f(x) as x approaches a is L." (That x ≠ a is to be understood.)

[@udayjordan4262]

and 4 no. y = mx for proofing that it is path dependent and so the limit doesnot exist

[@yawoa8268]

Per what I've so seen so far from your tutorial, it you apply direct substitution and get a fraction with 0 as the numerator, the limit exists but if both the numerator and denominator are 0 the limit does not exist?

[@Zero-vb6dd]

At time line 15:12, is it necessary to also consider the negative value?

[@dorachanda5873]

Does this mean when we find the limit to have the same value we continue with step three or only when our values are zeroes???

[@campeoncampeon4520]

¶ Definition. A variable approaches a constant as a limit when, after a certain point, the absolute value of the difference between the variable and the constant become and remains less than any preassigned positively number however small; and the constant is called the limit of the variable.

[@amexboss3114]

helpful please do more in this topic

[@drumman22]

Are there cases where direct substitution doesn't work at first but the limit still exists somehow? All cases you shown were if direct substitution didn't work then it was proving how it didn't exist.

[@AK-cy3ql]

what if at 17:48 limit in the question was not 0,0,0 but 1,1,-1, where would parameter "t" tend to now?

[@harmsyamial5392]

thank you so much mr chemistry

[@robertomontero2352]

at 4:10 wouldn't that equal 0/0 which would make it indeterminate?

[@_Tea_Tea_Tea_]

I am wondering the same thing

[@mushroom2493]

this was very helpful I can't thank you enough! treat yourself to something good ok??

[@thescholar12]

I have a question we know that if two limits are different The limit does not exist but what If we keep finding that the limits are the same then we need a infinite ammount of tries to prove that the limit exists if it does exist

[@0202823179]

The last example without using the t, the limit as y approach 0 is 1/2. Hence DNE. Same answer👍

[@tomasdobson4340]

Thank you so much, keep up the good work master.

[@marin8970]

Very helpful channel , keep going 👍🏻👍🏻

[@yaluman.]

on the last example y axis gives u 1/2 so we can conclude that dns

[@jovanmagtoto2428]

great video. Thanks for this tutorial sir. God bless

[@akshayshende8201]

In the very first question when I am finding limit using different paths then I am getting different values ? Please explain me.

[@AM-yd8en]

in min 12:16 in numerator it should be 2x^3 right?

[@olasadek3467]

6:54 you are saying no limits which is more rational then what my dcotor sent us which is that absolute value of f (x, y) = [ x^2/ (x^2 + y^2)] × | y | is all less or equal to a.v. Of y therefore the limit f when x, y tends to zero is 0.

[@tuannguyentranle7151]

I'm just a bit confused about why you use y^2 =x in 11:35' to solve this problem? help me pls and thank you.

[@suryashivaprasad73]

You could use pretty much any function of your choice and check if the limit exists, but if, even for one such function, you get a differing value, you gotta conclude that the limit doesn't exist. In this case, he chooses that function just cause it's typical to try parabolas (quadratic functions) and see if that checks out after trying lines (linear functions) and it just so happens that the limit spits out a different value when he does that. You can never actually prove that the limit exists this way (as there are infinitely many function/approaches you can take) but if you keep trying and find even a single function which doesn't give you the same value as every other function, you can state definitively and for a fact that the limit of the function just doesn't. Hope that helps you out :)

[@rushtamchakraborty3271]

Wow 😲😲 Really an awesome lecture on this topic.....👏👏❤❤

[@DivyanshSingh-vw8fz]

It really cleared my concept 😊.

[@daryagholami9725]

there is something I don't understand: why when we approach the origin from x=y direction ,we still write lim (x)-->0?

[@johannstrydom4450]

In the last example the limit can also be proven to not exist by approaching from the y-axis( answer = 1/2) and the x-axis or z-axis(answers = 0)

[@gregorybillias]

Such a great explaination and many different examples! Thank you a lot!!!!

[@Demonbacktony]

Coming in clutch for physics and now calc 3😩

[@WysonFyson]

am following from malawi .

[@themammothwhoflew8894]

what about when its not at the origin??