limit of the multivariable function (KristaKingMath)

► My Partial Derivatives course: www.kristaking...
In this video we'll learn how to find the limit of the multivariable function. We'll test the limit as we approach the point along different paths. If we get different values along any two paths, then we'll be able to state that the limit does not exist (DNE). Otherwise, if the value appears to be the same along every path that we test, then we'll have to use the precise definition of the limit for multivariable functions (epsilon-delta definition) in order to prove that the limit exists.
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If you could use some extra help with your math class, then check out Krista’s website // www.kristakingm...
● ● ● CONNECT WITH KRISTA ● ● ●
Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)
Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”
So I started tutoring to keep other people out of the same aggravating, time-sucking cycle. Since then, I’ve recorded tons of videos and written out cheat-sheet style notes and formula sheets to help every math student-from basic middle school classes to advanced college calculus-figure out what’s going on, understand the important concepts, and pass their classes, once and for all. Interested in getting help? Learn more here: www.kristakingm...
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[@BurritoGalaxy]

My calc teacher barely speaks english. So the combination of me being able to understand you AND you doing a great job at explaining is the best combo

[@kristakingmath]

Thanks Zanya! :D

[@ummokay]

Not all heroes wear capes

[@jterwilligerr]

Thanks! :D

[@138shreyshekhar2]

@@jterwilligerr??

[@abdelrhmangharib7401]

Thank you, i really love your passion to calculus and the way you explain it. you make me interested in learning more and don't stop it. Really thank you so much.

[@waleedkhan8590]

Your voice is so nice :o and your videos too. Thank you for this!

[@kristakingmath]

Waleed Khan You're welcome, I'm glad you're enjoying the videos!

[@kookships4367]

@@kristakingmath can you plzz tell me whem limit does not exist then can we apply precise def of limit delta epsilon def on it

[@ra29597]

And how do we find the limit in case it exists?

[@SpartanAesthetic]

First off thanks so much for saving all our lives in Calc 3. Most of your videos line up really well with Stewart's Calculus and prepare us for the problems in that book. This video kind of oversimplifies limits. You may want to walk through more approaches, and show squeeze theorem (minus epsilon-delta). So basically everything that would be required of us to find a limit in a reasonable Calc 3 class, minus epsilon delta because that's covered in the next video (and some classes like mine don't require it). Thanks again!

[@kristakingmath]

Thanks for the feedback, I appreciate it! :)

[@EdisonvsTesla]

Thanks a ton , you save me from being mathphobia , you have no idea to what extent do i love your video ❤❤

[@ahmadalaziz915]

You know, You actually helped out a lot this year of my first year in University. Also you did save me from having Summer studies. :D So thank you so much! I wished if my Professor is as good as you are. Million thanks to you. :D Right now I'm enjoying my great Summer.

[@kristakingmath]

I'm so glad I could help!

[@chrismondragon83]

Thank you so much! You are very helpful and probably one of the reasons why I will pass my calculus III class. I feel like I learn more from your videos than I do sitting in my class for 2 hours twice a week. Again thanks!!!!!!

[@kristakingmath]

+Christopher Mondragon I'm glad I can help along the way!

[@felikswielkopolan4001]

thanks a looot! u were the first person to explain it to me that i understand noow :)

[@kidusbahiru4369]

Best explanation. Thank you

[@shalinivijayekumar3515]

Thank you so much! I was really struggling in Calc 3 as a freshman and was thinking about dropping. However, your videos are an absolute lifesaver. I have no words to describe my gratitude.

[@kristakingmath]

Way to hang in there and work hard! I'm glad the videos could help. :)

[@MrSumansai]

your explaination is clear and undestandable and thank you for uploading

[@kristakingmath]

+Kannaya Suman You're welcome, I'm so glad it made sense!

[@victoriatran107]

You saint. Thank you so much!

[@glena1872]

You explained that very well, thank you so much!

[@kristakingmath]

+Glen A Thanks! Glad you liked it.

[@jufbjfuyk]

Thank you. Awesome work.

[@omgitsibrahim7712]

ur so good at this well done

[@ghostf6321]

I'm learning this in Calculus 3 right now at my University and your explanation is much less confusing than the way my professor(who is actually a grad student) tries to explain it. Do you have more examples of this somewhere?

[@kristakingmath]

+Jason Frates I don't have a lot of different examples of this same kind of problem yet, but I'm hoping to make more!

[@jtbanner7220]

+Jason Frates Are you in my calc 3 class at GA Tech? lol

[@ghostf6321]

Ja'Quan Taylor
Most likely no, I go to Clemson. Your guess is close but not exactly lol.

[@jonathanaguilar990]

+Jason Frates I'm only in Calc 1, doing calc 2 in the summer. May God bless me lol.

[@ghostf6321]

Jonathan aguilar
A lot of people take calc 2 at a tech school because the way they grade it at university level(atleast at clemson) is brutal, they give you little to no mercy if your algebra is wrong even if your setup and calculus is right.

[@nosliw9911]

Explanation on point! 👏

[@kristakingmath]

Thank you Nosliw! :D

[@marierymdtiger8674]

Thank you, this helped me alot! Greetings from Sweden.

[@kristakingmath]

i'm so glad it helped!!

[@AnaximandroAndrade]

Amazingly clear and simple explanation!!!! Thanks!

[@kristakingmath]

Thanks! I'm glad you liked it.

[@adamhaigh9927]

Holy cow! Thank you! My book had no illustrations for this, bout to subscribe to your channel for sure! haha

[@timxu3536]

Thanks! my calc professor is terrible so this was really helpful

[@michaelquigley9052]

Thanks so much! All of your videos I've watched have been so helpful!

[@kristakingmath]

Yay! Thanks for letting me know. :)

[@binkshimself]

Great video. You explained this material very well.

[@mshary8943]

Direct to the point. Great explanation 👍🏻

[@kristakingmath]

Thank you so much, Mshary! :)

[@da_druuskee7709]

girl, in my eyes, you the baddest. thank you!

[@nobadragoon6499]

Is there any way to find out beforehand whether the limit exists just by looking at it? How do I know whether to start by using the definition or by "along different path" method?

[@SarahGodfrey23]

thank you this helped so much!!

[@kristakingmath]

you're welcome, i'm so glad it helped!

[@Hgkbukk]

One of your best and clearest video! Great job!
Understood everything! :D

[@kristakingmath]

Thanks! :D

[@noranhosny1598]

This is a really good ,smart way to solve the problem.Keep the Awesome Work ;)

[@kristakingmath]

+Noran Hosny Glad you liked it!

[@beacampos13]

krista king you are my queen

[@Anand-wi4yb]

Your voice is just awesome!! Great explanation

[@talhaskhan37]

Super clear explanation, thank you. How would it work if we approached the line from y=mx? What would you need to end up with to know that the limit does/doesn't exist?

[@kristakingmath]

+uoenodoe If you were approaching along that line, then you'd plug mx into the function everywhere for y, and then evaluate the function at the point you're approaching. If you get the same answer that you get when you approach along every other path you try, then you'd suspect that you'd found the limit, but you'd need to use the precise definition to prove it. If you get a different answer for any one of the paths, then you know right away that the limit does not exist.

[@ishaanbahalkar3479]

Thanks for this video!

[@kristakingmath]

You're welcome, Ishaan! :)

[@ngusumakofu1]

Thank you so much, it was almost impossible to follow in class and I couldn't find this on Khan Academy.

[@kristakingmath]

+Advocatus Diaboli I'm glad you kept searching and found what you were looking for!

[@stvnhentzen]

Great explanation, this helped me a lot. Thanks!

[@kristakingmath]

You're welcome! So glad it helped! :)

[@MatEntertainment]

Excellent video and explanations, thanks!!

[@kristakingmath]

Thank you!

[@UnknownUnknown-us2cv]

What Happens when i get at first limit infinity? can i just tell that limit doesnt exist? or should i check the second lim?
does inf considered as limit?

[@cirolo98]

Life saving. Great work!

[@kristakingmath]

Thanks, Ciro! I'm so glad it was helpful! :D

[@ThePinoyMamba]

Thanks Krista!!

[@Ensign_Cthulhu]

Neat! Do you have an example, or can you create one, showing how to approach the limit along a particular line or curve? I'm assuming that for an approach along y = f(x), you would replace all the y in your original function by whatever f(x) was, do the arithmetic accordingly and then take the limit of that new function all in x as x approached zero. Just eyeballing it, this would give zero divided by zero for any f(x) = x^n, i.e. undefined, which is neither -2 nor zero (if you happened to do either of those first) and therefore the general limit would not exist. Yes?
Of course the tricky philosophical question is this: let us assume you approach neither along x nor y axis, but along two curves; if they both return limit values that are undefined (either infinity on infinity or zero on zero), are they necessarily "the same"?

[@MuhammadAbdullah-sw9ix]

You're so good

[@binge8334]

Thank you Krista king

[@viniciusbarbosa9633]

Thanks !

[@Jer-33_3]

So i'm getting ready for my cal 3 final and this was the way that i understood how to do it, but on our example test with solutions they solve it by assigning y x values. For example, for the function (x^2y)/(x^4+y^2) they let y=x and y=x^2 to get the limit to 0 for (x^2x)/(x^4+x^2)=0 and the limit to 0 for (x^2x^2)/(x^4+(x^2)^2)=1/2. I don't understand why they chose x and x^2 for y and how they simplified the second function to get 1/2 instead of 1. Can you think of why they would choose to do it this way? And would I be incorrect to do it the way that you show in this video? I get DNE either way since I end up with a 0 in the denominator doing it your way. Thank you!

[@ravishankariitbhubaneswar8622]

can we draw a graph of two variable function which you have taken in this video?? if yes how to sketch??

[@gene546]

5:10 But, also, y approaches (0,0), so y should be zero not -2. I will appreciate your response.

[@kristakingmath]

y is approaching (0,0), yes, but since you get y^2 to cancel from both the numerator and denominator, it tells you that there's a removable discontinuity at (0,0), so that first expression will approach -2. If the y's didn't cancel out, you'd be correct, but since they do, the value does approach -2.

[@gene546]

Thanks again, and thanks also for your commitment to teach math

[@johallyw3]

It helped a lot! Thank you!

[@kristakingmath]

+Johally sa You're welcome, I'm so glad it helped!

[@danielbenshemon6379]

WOOOOOW. 🖒🖒🖒🖒 👏👏👏👏👏 I'm speechless. You are amazing.

[@prateekgurjar1651]

You are doing a really great job Krista, Thanks A lot, you saved my skin in the test. And your voice is beautiful too

[@lorenzosandoval7314]

Do you have a cape?? YOURE AMAZING

[@jeffciaccio2463]

Can anybody help?
Lim -> (pi, 0) of (xy - pi*y)/( tan(x) * sin(y) )
Looks like the lim = 1, so we need to use the epsilon-delta definition, but I just don't see the proper substitutions

[@AliAhmad-yt2tg]

thank you maaaam

[@kristakingmath]

You're welcome, Ali! :)

[@SpinfireCreativity]

Thanks again CalculusExpert!

[@kristakingmath]

+Douglas Graham Aww thanks for letting me know!

[@shawnnyhus2193]

where does the feftover right go?

[@salehahmat7726]

Hı teacher. can you help me with this exercise: if line l passes through point (1,2,3) and is perpendicular to the xy-plane, what are the coordinates of the points on the line that are at a distance 7 from the point p (3,-1,5?

[@user-nx7hs7kz3l]

excuse me. -2 is a y value or x?

[@neylsonrodrigues7350]

Thank. I like your channel and it is really helping me in my calculus course. How can I support the channel more? you don't have any merch.

[@kristakingmath]

Thank you so much, Neylson! I'm glad the videos are helping! The best way you can help is by subscribing to the courses on my website, or purchasing my courses on Udemy. :)

[@SSS20025]

Why can't we use the same method in one variable function?

[@Taricus]

Let y=cx, do one limit and check to see if the limit depends on the path taken... :P

[@EngineeredAdventures]

Notation that you are using while showing the x and y coordinates wrong. You should put the arrow where the value approaching the positive infinity. Best regards.

[@chibzzz]

what does the limit mean

[@sivavara]

what for limit(1,-1)

[@hassans8169]

Wow Your explanation is so profound.
BTW which software you use to tech. :)

[@naimulhaq9626]

I wonder why is the function not plotted to see how (0,0) is approached, then arbitrary testing from other directions will not be needed, and actual limit of the function will become obvious.

[@ntuthukomthiyane5017]

thanks a lot

[@kristakingmath]

+ntuthuko mthiyane Glad you liked it!

[@clarastezowski517]

You are sent from above

[@soorajkrishna3674]

When we aproch the point through a line do we need to take limits from both direction of the line wrt to the point like lhl and Rhl when we aproach through x axis

[@SSS20025]

We always take a line which passers through the point. So it's always continuous and the limit exists. You only have to approach from one side.

[@ahlinad1221]

Thank you so much :) So the concept of approaching from different directions is such that if 2 directions give different limits, then it doesn't exist.

[@albatrosmundodeaventuras6873]

lim(x,y)-(0,0) x4-y4/x2+y2 solucion

[@studytreasure95]

nice useful Video

[@cosmickitty9533]

Thank you! Is this also know as the two path test?

[@kristakingmath]

Yes it is! :)

[@cosmickitty9533]

Thank you :)

[@ZuoCruz]

Better explanation

[@kipkiruivictor3320]

2.26

[@shideshpatil4796]

*2:09 * it is curve

[@taimalachkar714]

made my life easier

[@kristakingmath]

Yay! That's what I'm hoping for. :)

[@22sungho]

Thank you SO much (,,;

[@TheChondriac]

Your voice sounds very similar to ViHart's voice! She's another math TH-camr.

[@sphesihlepraisegod955]

jst love her

[@yazan13]

YESSS

[@Bo-jl8jr]

thumb up before watch

[@nabiloov5637]

you are better than my fucking teacher ....
i just wanna thank u

[@FALprofessional]

Now, would you mind doing one that requires an epsilon-delta proof.
NOT! I will pass on that nonesense. Thank you for the explanation.

[@kristakingmath]

+l FALprofessional l LOL

[@ImaMemeber]

Thanks mom

[@kavinduadhikari5881]

Oh thanks god. God saved me, and you are the angel who was sent by him

[@felikswielkopolan4001]

omg voice like hannah montana :o

[@zelikris]

marry me

[@shivambansal5725]

U make it too simple to understand.

[@kristakingmath]

I'm glad it made sense! :D

[@SonatinaClef]

Ooh yes back to calculus and not the simple algebra. No offense to anybody taking that or don't understand it