Limits of multivariable functions

In this video, I showed how to compute the limits of some multivariable functions

[@hvok99]

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

[@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

[@just4simplegg428]

I love this guy's charisma

[@BlueSiege01]

Thanks for the Videos sir!

[@WAFBECH3]

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

[@itsmepratish]

best in the job never stop learning

[@sbahlenontobeko5844]

You're the best sir

[@nonentity168]

Great tutorial

[@ayeshaaaaa3623]

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

[@SazisoVilakazi]

great video

[@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!

[@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

[@twarisaninyoni-pf7sk]

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

[@colina64]

THANKS

[@tinotendalearnmore4014]

He’s the goat

[@nadkhaa8360]

u r second to none.

[@petelok9969]

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

[@thenovalabs]

Thanks

[@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

[@BP-me7lj]

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

[@Folorunsho3729]

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

[@ALIENGOATMESSI]

8:18 will help you understand

[@DeepCoder786]

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

[@wbell539]

Wish I had seen this about 60 years ago!

[@PrimeNewtons]

Lol 😆

[@CharashGanja]

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

[@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).

[@heathjokerledger101]

How to use L' hopital's rule here ?

[@JPL454]

You don't

[@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