Limits of multivariable functions

[@hvok99]

You are an excellent teacher. Thank you for your clear and passionate presentation.

[@just4simplegg428]

I love this guy's charisma

[@huntern5813]

fan from ethiopia, i am electrical and comp engineering student you've been helpfull very much . i hope you'll make more videos in calculus III

[@WAFBECH3]

it became plain and simple till after i heard idea of applying the directions. thank you sir

[@caiotorres6156]

amazing teaching

[@Bradley-nj3zy]

I have to admit, I just love your channel

[@thabomandlenkhosi3224]

You always makes it easy

[@chabotakanene-ll1dk]

The Prime Newtons, you're excellent, i love our content from you, so, this is what we should be doing, when showing those other videos, I would appreciate if a link pops onto the right upper corner of the video to each video clip shown as a reference

[@itsmepratish]

best in the job never stop learning

[@SIDDHANTCPATIL]

Appreciate this video. Thanks sir ❤

[@THEoneandonlystika]

8:18 will help you understand

[@sbahlenontobeko5844]

You're the best sir

[@ayeshaaaaa3623]

where can i find the 2nd video?? the polar coordinates one

[@DestinySanyangowe-y8e]

THANK YOU SIR CAN YOU PLIZ DO ANOTHER ONE OF EPICILON DELTA PROOF OF MULTI VARIABLE FUNCTION

[@nanamacapagal8342]

Question: when it comes to limits like those in the third question, how do I know which substitution to make, and how long to keep testing?

[@pedrogarcia8706]

I think you just pick a function that satisfies the point you're looking for the limit at. So in this case it would be any equation where (0,0) is a solution. Then you check multiple functions hoping that your answers are different so you can write that the limit doesn't exist. It sounds like if the functions you choose keep having the same answer, there's another method to determine whether the limit exists using polar coordinates that I'm not familiar with. Hopefully that video will come out soon!

[@krishnasimha8097]

for a generalised answer keep y =mx^3 and u can see that limit doesnt depend on x or y

[@negativexfinity6778]

Good stuff

[@twarisaninyoni-pf7sk]

When we factor out y^2 in the denominator aren't we supposed to get y^3 instead of y^4?

[@BlueSiege01]

Thanks for the Videos sir!

[@aguyontheinternet8436]

when limx=limy=n, why wouldn't it make sense to make x=y, since they both approach the same value in the limit?

[@Lilliana1]

We are talking about if it will approach the limit. We are checking that not the other way around

[@petelok9969]

Hi, do you have a link to the puzzle thing you mentioned at 3:27? Best Wishes Peter

[@SazisoVilakazi]

great video

[@nadkhaa8360]

u r second to none.

[@BP-me7lj]

why did you not take this path method in question 2?

[@wbell539]

Wish I had seen this about 60 years ago!

[@PrimeNewtons]

Lol 😆

[@tinotendalearnmore4014]

He’s the goat

[@CharashGanja]

i think you should give us a example like the third example but limit exists there

[@thenovalabs]

Thanks

[@nonentity168]

Great tutorial

[@ubidubium5806]

in the 3rd problem, let's have y = x and see what happens.

[@deespace3744]

he has already considered that case

[@Salamanca-joro]

Yeah that's what i did and I got 1/x^2 which is 0 at the end so the limit is 0 I guess

[@hipepleful]

If you were making a joke, i loved it.

[@Folorunsho3729]

Only if I could get a sure physics plug like this too😫

[@DeepCoder786]

Sir you put 0^6=1 But it return zero in Chat gpt

[@colina64]

THANKS

[@TheEvilHacker1997]

Or you could just use l'Hôpital 6:15 and be done in 7 steps

[@wwbbcg01]

L'Hospital's Rule only works on single variable functions.

[@TheEvilHacker1997]

​@@wwbbcg01The variables are the same number

[@heathjokerledger101]

How to use L' hopital's rule here ?

[@JPL454]

You don't

[@dretrotbeats3961]

uli bho ngat iron monkey watiiika mtika.🤪🤪🤪

[@samuelfemi2227]

Why can't we use l'hopitals rule?

[@Natolino83]

L'hõpital's rule is only defined when we're working with only one variable (and some other conditions).