Limits of Multivariable Functions - Calculus 3
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- Опубликовано: 29 сен 2024
- This Calculus 3 video tutorial explains how to evaluate limits of multivariable functions. It also explains how to determine if the limit does not exist.
Lines & Planes - Intersection: • How To Find The Point ...
Angle Between Two Planes:
• How To Find The Angle ...
Distance Between Point and Plane:
• How To Find The Distan...
Chain Rule - Partial Derivatives:
• Chain Rule With Partia...
Implicit Partial Differentiation:
• Implicit Differentiati...
________________________________
Directional Derivatives:
• How To Find The Direct...
Limits of Multivariable Functions:
• Limits of Multivariabl...
Double Integrals:
• Double Integrals
Local Extrema & Critical Points:
• Local Extrema, Critica...
Absolute Extrema - Max & Min:
• Absolute Maximum and M...
________________________________
Lagrange Multipliers:
• Lagrange Multipliers
Triple Integrals:
• Triple Integrals - Cal...
2nd Order - Differential Equations:
• Second Order Linear Di...
Undetermined Coefficients:
• Method of Undetermined...
Variation of Parameters:
• Variation of Parameter...
________________________________
Final Exams and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
/ collections
Final Exams and Video Playlists: www.video-tutor.net/
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.
Euchariah Brown got a 78 and ended the class with a B
@@ampleeeeeeeee thanks lololol
@@lidyasolomon5557 Awesome; I’m glad you could pull it out! 👍
@@PunmasterSTP lmao thanks I graduate with honors we good 😭 how r u
@@lidyasolomon5557 That’s excellent to hear! I’m doing fine myself.
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???
guys I need help
When we can use direct substitution and when we can't?
You are single handedly giving me my math credits towards my degree 😂
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
Thanks
Thank you for the timestamps!
you are angel something thanks
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.
How’d the rest of your class go?
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.
@@mrbanana6464 accurate! Like the parameterization at the end? Lost me.
I think it depends on what you are doing, for math major this is not enough, but for engineering studies, this is very helpful
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!
right
Same here, he made Calc II a breeze. Calc 3 is harder though :p
@@anirudhbukka5413 college
@@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
Are you huys seriously self-teaching calculus????
I mean college courses are hard enough
can anyone explain in 16:35 along y-axis we have x=0,z=0 don't we get a limit of 1/2
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!
16:43 last example the y -axis when z=0 and x=0 its equal 1over2 which not zero
Yea bro. So we can conclude that limit does not exist at that step
Yea I did the same too
But he is trying to teach us more ways to solve incase this one didn't work in some other cases
@@pranavbhanot816 yep
You’re right
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?
ya, I got that too. In that case the limit doesn't exist
Is there a limit as to how many topics you can cover? Keep up the good work!
The limit approaches infinity
It DNE
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.
yeah, for the y-axis I got 1/2
@@付相龙-b2t yes same
Yeah that's right 👍
There itself we can say that limit doesn't exist
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.
Calc 3? im so far gone from calc 1 trying to find an answer from a test... good luck Uni students doing this.
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?
right
Yes I got the same too
@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
It does not exist. If it fails to be the same from whenever we approaches, it's not existent.
@@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
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?
i got the same question
i did thge same thing
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?
You are the reason why am still surviving calculus
Your videos are fast and to the point! Thank you
I'm not even a chemistry major hahaha
But the real problem is when you use direct substitution and it's undetermined. Then use approach by different axis and curves, parametrization etc... and all limits are equal to something. How do you find the limit then? T_T
In this situation you have to use the precise definition of the limits of multivariable functions.
Kudus to d create tutor on RUclips. 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.
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 ?
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...
Which degree are you doing that can be explained in a basic multivariate calculus tutorial video
@@akshatsrivastava4280
Math 209 Calc. III University of Alberta
I’m in Algebra 2 as a sophomore and I understand this. That’s how good this guy is at explaining math.
right
Wtf. We finished Calc AB as a sophomore lol
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.
@@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.
The last example helped me on my quiz so much for proofs!! thank you!!
and 4 no. y = mx for proofing that it is path dependent and so the limit doesnot exist
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?
I dont get part at 10.30 , how suddenly he makr y² = x
This is absolutely amazing!!!!!!!!!!!!! Why don't we have teachers like you in school????? 😭😭😭😭 life would've gotten much easier!!!!! 🥺
if the answer of direct sup. zero over zero it always dne?
Thank you! I was really stuck in this 3 variable limit at the origin, but this gives me hope to get an answer:)
Isn’t 3:57 cannot be computed since it is 0/0
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
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
how about this
lim (x) -> 0 : 1/2x
is it undefined?
yes is inf
Love your videos, can you make a Calc 3 final exam review video? Thanks!
The last limit does not exist, it is not enough to check just one path.
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
Why am I watching this? I'm in AB Calculus
It only gets harder from there. I miss AB calc
@@kennyd4223 whats the point of patting yourself on the back in youtube comments?
Josh Music what’s the point of naming yourself “Josh Music” if you have no subs or any uploads?
Josh Music also, I wasn’t “patting myself on the back” there, I was merely stating facts about calc in general. I don’t want to see you pop up on my phone again. Have a nice life
@@kennyd4223 lol very mature 😂 its my name and youtube is connected to google, smart guy
The last example without using the t, the limit as y approach 0 is 1/2. Hence DNE.
Same answer👍
Thanks you for... I'm from Pakistan
Thank you very much! haven't been paying attention in class lately
you are right
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 RUclips TV with the Organic Chemistry Tutor.
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
I still remember doing this back in my highschool in Canada! Thanks for bringing back my memories!!
highschool?
@@assaultszn3557 I started studying calculus when I was grade 6 and then i happened to advance through math in HS 🙂
@@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
don't you guys normally only do Calc.1?
@@metawhirl4609 smart-ass
In the very first question when I am finding limit using different paths then I am getting different values ? Please explain me.
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.
exactly i tried it too and with lim y approaches 0, the result is 1/2 thus proving the limit doesn't exist :)
Yeah that's correct ☺️
There itself we can say that limit doesn't exist
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.
very important point. totally agree.
Thank you sir one video solved my all problems
there is something I don't understand:
why when we approach the origin from x=y direction ,we still write lim (x)-->0?
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.
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.
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
sertöz teorem bilseydin bu kadar uğraşmazdın.
How many curves do we have to keep trying?
As many as it takes for you to find a limit that's different that the previous ones
@@bolzac2168 but what if limit exists and it is zero
is here eone teacher or multiole teachhers for multiple subjects if same teacher then it is miracle and i dont believe on it hh
I have a question: What if, when we directly substitute the values of (x, y, z) or (x, y) into an equation and get a number over zero, for example 3/0, and the answer becomes undefined? What should we do? Is there a method for dealing with this or is the answer just undefined? please answer as soon as possible !!!!!!!
I’m only here because of Mean Girls
so, got a question. my teacher said for a limit where x->0 and y->0, of say... (x-y), you could break it into: lim (x->) [lim(y->0) (x-y)]. is this correct?
lim where x->0 of lim where y->0 of x-y ?
what if the limits are changed , then we have to apply those points that satisfy the domain bcz just say e.g the limit is 1,-1 then we have to check from those routes that satisfy 1,-1 like x=-y as x=1,y=-1????
lowkey just sounds like if you have 2 zero values it is always DNE because the 3rd value cant be 0. But maybe not
Can someone help me with this limit? I just can't wrap my head around it xD : lim(2x^3-y^3)/(3x^2+4y^2) as (x,y) --> (0,0)
thank you so much. this saves me so much since im a visual learner
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?
The last example, when y approcahes 0, the answer is 1/2 which is different from when x approaches 0. So DNE.
Good teaching sir
I am indian
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.
for the last problem wouldn't y-->0 be 1/2 and not zero? What's the reason it wasn't checked
¶¶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.)
Why do we always approach the origin! Can we have more examples when we do not approach (0,0)!
If the y-axis,x-axis and y=x all equal the same number, how do we know when to stop?
Hi! I wonder how can i know which method to use? Like how could i guess that I should use the x=0 method or x=y?
My exams in 36 hrs and I haven’t studied shit. Pray for me guys.😓
¶ 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.
6:59 is that a limit or not now ?
THIS VIDEO IS A LIFE SAVER ,THANK U SO MUCH
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.
In the last one when I tried approaching from the y-axis I got 1/2
If you can find it directly with direct substitution, why is the exercise finished? Is that proof enough that it exists?
Tutor
At last sum if y applied it in y axis u get the lim y->0 as ½ like that we can prove right
16:32 approaching by y axis wont give you 0 but 1/2 .
this is all busy work 😭
I always wonder, why the channel name is The Organic Chemistry Tutor when a person who is teaching is actually a gem in mathematics.
7:25 but doesn't this only show one path gives a limit of 0? what about all the other paths?
12:18 I must really struggling if the graph here made me laugh, looks like a 😊
Gosh, your vid always help me, love your work, very simple yet easy to understand 2 hours of my lecture
on the last example y axis gives u 1/2 so we can conclude that dns
At time line 15:12, is it necessary to also consider the negative value?
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.
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 :)
@@suryashivaprasad73 many thanks
at 4:10 wouldn't that equal 0/0 which would make it indeterminate?
I am wondering the same thing
2 days to sem 1 exam ...
💀 hope these videos will save me !!
Coming in clutch for physics and now calc 3😩
Any videos on functions of two variables 🥺?
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 :)
in min 12:16 in numerator it should be 2x^3 right?
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.)
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 👍🏻
at 7:42 is it just me who feels this way or he doesnt want that sum to have a limit?
On the last problem can we simply put x,z=0 and check for limit? I get limit to be 1/2 which is not 0 => DNE?
I think the last one use yaxis would work