Multivariable Calculus: Showing a Limit Does NOT Exist

[ssaleem92]

awesome video, could you do one that includes a z variable? i'm having a lot of trouble on those!

[mytwohands]

Does anyone know if Patrick's done any videos involving proving the limit does exist? Those are much trickier to me (with the whole epsilon/delta thing) ...

[patrickJMT]

@mytwohands i do an example where the limit exists, but it is just the algebraic sort of problem. i do not actually use the delta-epsilon definition. i reaaaalllllly should make some videos on those...

[JaktheAtheist]

@patrickJMT

Yes you really should! I miss your videos so much from Calc 2. I've practically been on my own with Calc 3. That's fine, but it's much better when I have someone who can actually explain things in a coherent way up front. I can figure out how to do things on my own, but I find myself walking away with a better understanding on the subject if you or khan academy has a video to help.

[moro1891]

@patrickJMT

We all think you should REALLLLY do it, and so do you, so please do ASAP when you have some spare time please :D

[TheNumber2Pencil546]

yes! the example you did was my homework problem

[earthyearth]

hi! can you try doing x+y/(2x^2+y^2) please or anyone here :(

[desertkid18]

you are the man! period

[speedboarding100]

I have no idea how to express my gratitude for your videos! My professor is literally worthless when it comes teaching. You are the best man! Thanks so much

[patrickJMT]

@speedboarding100 glad i could help : ) tell your friends!

[redhotkido]

how to learn math concepts? Pat JMT

[pepteamsergi09]

So.. how does the graph looks like? Good video.. ty!!!

[nikan4now]

you're a great teacher ..thanks for the effort...do u have any videos regarding the gradient ...i sometimes get confused about when this operator shows the normal to a surface and when it gives the direction along which the derivative is the largest...many thanks in advance

[patrickJMT]

@nikan4now yes, there is stuff about the gradient

[dragonzball24]

A+ for my advanced calc paper all year at uni . thanx a lot for ur help dawg

[raincawili]

bia dke lee mi ka hau :)))))

[patrickJMT]

@raincawili i do not know what you are saying ; )

[patrickJMT]

@raincawili but i assume it is nice from all the :))))))  !

[solidiquis1]

What's the difference between single variable and multivariable calculus?

[patrickJMT]

@solidiquis1 a single variable versus a multivariable

[solidiquis1]

@patrickJMT But I'm doing single variable and there are multiple variables :/

e.g. Implicit differentiation.

[patrickJMT]

@solidiquis1 well, the variable (usually y) is actually a function of x; so that there is still only one independent variable

[MrDevin666]

Have you taken your SAT Pat? If so, what was your score?

[patrickJMT]

@MrDevin666 i scored 1,000,000

[MrDevin666]

@patrickJMT You must be from BundyLand.

[MrDevin666]

@MrDevin666 I'm calling the fucking cops.

[simplylatina87]

this james stewart book sucks donkey balls. i only wish i wouldave discovered these videos sooner =/

[patrickJMT]

@simplylatina87 i think it is a pretty good book personally

[AliAlzaidi90]

@simplylatina87 agreed

[patrickJMT]

@AliAlzaidi90 well, i taught myself calculus from that book so i do not think it can be all bad

[dmed312]

@patrickJMT Okay, so did you teach yourself calculs solo, or did you have tutors and teachers in college? Do you have an official degree? I'm asking because I too would like to teach myself, no college, no tutors. Just me and a good book.

[patrickJMT]

@dmed312 well of course i had teachers, never a tutor. college is learning to basically teaching one's self though. a professor can not magically get all crucial info in your head in 3 hours a week, they can only hit the highlights and answer intelligent questions that a hard working student comes up with. the more clueless people think the opposite though i think...

[2010lovejustin]

y r you making it so complicated??



[patrickJMT]

@2010lovejustin cause i like to hear you whine

[pilot233a]

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[h3sl]

totally agreed please sir patrick more videos about multivariable calculus :( ..

and by the way .. does the same method works for proving that the limit exist ? assuming that there was no conjugate .. i mean in " james stewart " book they only use the method of using definition to approve that the limit exist ....

[HelloRoshan]

I'm currently taking calc 3 as a senior in highschool, and YOU sir, are saving my life.

[GossipXGuy]

who watched this because they wanted to understand why the limit did not exist in mean girls>.<

[ClaudiaG91]

THANK YOU

[onlnr]

Has Patrick made anymore limit videos for multivariable calculus? I have some pretty complicated examples in my workbook that are a little more complex than the example in this video!

[firewire67t]

Patrick, when I finish school and get "properly" employed I'm sending you a fat donation, I can't thank you enough for what you do!

[spartan387]

please make more linear algebra and multivariable calculus and differential equations videos please... triple please..... limit of please as please goes to infinity with respect to please... pretty please ^_^

[jsudbang]

Wow, thank you so much. In my recitation my TA practically doesn't speak english, we can never ask him questions because he doesn't understand us so I was having trouble with some of these concepts, but this clears it up so much.

[jessand01]

Help me please..!!!! i have to demonstrate that a limit exists by using the squeeze thoerem, but i never understood it!!!...instead i would like to use polar coordinates, is it a valid way to demstrate that a limit exists?

[ilikeche2]

Amazing what a difference having an English speaking math teacher does.

[kyladamsmovip]

What would I do for the function (x^2+y^2)/(x+y) as (x,y)->(0,0)? I have to prove it doesn't exist but every time I try to approach the origin from a different direction/along a different curve I get 0 every time! What do I do?

[mattdelhey]

@kyladamsmovip try sin(x)

[rchen972]

cmon guys he has 20k views and only 120 likes??

[vplof]

another good way is to replace with y=mx and then it shows that the limit does not exist. because "m" can be any number.

[fchang08]

Wow I just watched this video and I can't believe how easy you make it!! Can you come teach my class???

[InfernalKamikaze]

I LOVE YOU!!!! You've been basically coaching me through college math since calc 1. Thank you thank you thank you.

[patrickJMT]

@InfernalKamikaze you are very welcome ; )

[exorcismproductions]

I want a shirt that says i fucking love patrickJMT <3

[barynew]

Hi Patrick!

I've seen your video, it was great.. but i've got a function, which i can't solve. Can you help me? The function and the question are: f(x,y)=xy ln(xy). lim x,y->0,0 how can I figure out that limits are exist? If I approach along x axis, I don't get the right solution, and if I approach by another function, y will always zero.

Thanks for helping me :)

[Mustang5Speed]

Seriously, you never fail to be flawless in your teaching, thank you!

[ObscureRealm]

I like the ratio of likes to dislikes. 100:0 Same as infinity:0 :D

Great vid, very helpful!

[bigtymer9778]

Ok what if the limit as x approaches 0 also = 0(instead of 1) like the limit as y approaches 0? Is the limit still proved to be nonexistent?

[macrocec]

if I take more advanced math classes, im afraid there wont be more patrick's videos on youtbe about more complicated stuff. that makes me sad :(

[patrickJMT]

@macrocec yep, only a bit of diff eq and linear algebra at the moment : )

[macrocec]

@patrickJMT thanks for all though :)

[pamepelle]

Hi Patrick, could you show more examples from multi variable limits please?

Cheers!

[MsCs12345]

fanx man getting my mafs on

[erickarule4]

If I give you $100 and 3 square meals a day, will you come live in my basement?

[patrickJMT]

@erickarule4 let me think about it...

[ECENoorAlsawadi]

THANK UUUUUUUUUUUUUUUUUUUUUUUU .. u make it sound so easy :D

[hendsem]

but what happens if it approches from the negative limit of discontinuity because of both lechatelier's principle and lhospitals rule that says that if an apple drops from a tree it will hit newton in the head.

[okoloptttify]

I fucking love you.

[patrickJMT]

@okoloptttify thats what i like to hear

[ajskdlfla]

@okoloptttify in bed

[bithboyband]

I just wanted to say how much I appreciate your videos!

[patrickJMT]

@bithboyband glad you like them

[sabah6704]

exellent

[footballer671]

how about lim as (x,y) --> (0,0) of (x^2)/y ? i couldnt use the origins cause i'll get x^2/0. thanks.

[utubegay1]

more multivariate calculus videos please!!

[hawanddoo]

i think i should start paying instead of my college, i dont know wht my calc teacher babels about for 90 minutes lecture

[cooptroop123]

how about to show it does exist?

[masterjim2007]

what would be the answer if you were approaching from (1,0) instead of (0.0) ?

[SgtSinister]

Just wanted to let you know that your videos are getting me through calculus and are a BIG help. Now I just need some similar videos for chemistry :/ Can you make those or recommend some? haha

Just so you know your playlists are severely out of date. It'd be a big help if all these limits videos were on one playlist.

Also, have you thought about putting these all together on a DVD and selling them? I would gladly pay for something like that!

[patrickJMT]

@SgtSinister not sure about chemistry. i know the playlists are out of date. i hate updating them.

i am in the process of getting my videos set up for download; they should be available in a week or two (hopefully). i am also going to have an app out soon for iphone/ipad!

[geovaniluna]

@patrickJMT

PLEASE TELL ME THAT YOU HAVE A VIDEO ON HOW TO GRAPH CONTOUR MAPS.....MULTIVARIABLE CALCULUS

[5185988519]

@SgtSinister There's videos made by people called the Educator. Just search for the topic you need help on in Chemistry and then "Educator" on YouTube, and it will lead you to a free tutorial. Make sure it's red and a guy named Professor Goldwhite teaches it. The Educator helped me tons when I was in Chemistry and Prof. Goldwhite is British.

[jiaxiking]

quick question, how do you prove a limit does exist? Maybe X=0 and y=0 both works, but when you set it to x=y, it doesn't work. How can you determine whether it actually exist?

[patrickJMT]

@jiaxiking well, you can either use the definition (which no one likes) or sometimes you can do some algebraic justification (like factor and canceling). if you get different values from different directions though, it for sure DOES NOT exist

[MansKlingspor]

@jiaxiking Switch to polar coordinates and evaluate the limit as r (the radius) approaches 0 and the angles vary freely. Since the angles vary, the limit is evaluated along every possible path.

[xkrntylsekkix]

lol i rather pay you like 79 cent per video

of all the concepts i need to know

then pay over 1200 for a professor

who doesn't know how to teach and

wastes 2 hours of my life 3 times a week

with a discussion leader 3 hours a week

that is equally as confusing as the professor.

[patrickJMT]

@xkrntylsekkix ha, i prefer that scenario too : ) i am just a poor guy making videos with low quality equipment in a dark room of my villa!

[VWinUgo]

patrick i am aware you hear this all the time but i love you and what I believe you stand for. thank you. take care and god bless

[patrickJMT]

@VWinUgo thanks : )

[kwonj]

5:13 pen not liking mC

[garnett114ever]

Amazing! For everyone stop crying about more and just thank him. He's doing it for free, he really likes to teach, and thats rare.

[cdslone]

i just wanted to say thank you so much for taking the time to make these videos! they've really helped me understand some concepts better this semester.

[ursofunny404]

how do we know which approach curve to choose?

[kyledr1998]

@ursofunny404 as long as (0,0) exists in that curve/ the curve approaches (0,0), you can use that curve.

[ursofunny404]

@kyledr1998 thanks so much :)

[cruthybabie]

thank you! this is a lifesaver...

[rockoholic91]

where can i find more difficult examples of this?

[unknownlove19]

you said you were gonna make more limit videos for multivariable calculus :(

i have a midterm tomorrow :(

[InfamousShogun]

@unknownlove19 did you pass?

[unknownlove19]

@InfamousShogun lol of course i passed! more than passed. i love math although i don't need to take any more courses :)

[macrocec]

@unknownlove19 its been around a year, how did that midterm go???

[wwecrazy213]

more multivariable calculus videos plz =D

[unknownlove19]

THANK YOU SO MUCH

AHHHHHH

[mjcowley]

Very very helpful. Thanks

[PaperChaser01]

what about proving a limit DOES exist?"(2x^2sin(y))/(2x^2+y^2)­" ?

[Leemacdizzle]

If it exists you need to prove so using an epsilon proof. Look for the procedure online and you should be able to figure it out.

[DTAify]

What happens if the original equation was x/(x^2+y^2)?

When you move along the x axis, y stays zero.

You get 1/x. What then?

[PaperChaser01]

lim 1/x as x>0 = infinity

[PaperChaser01]

...i think

[novatodeguitarra]

When you got x^2+y^2 the best is to use polar coordinates

x=ρ*cosθ

y=ρ*sinθ

so x^2+y^2 is ρ^2(sin^2(θ)+cos^2(θ)) and that's just ρ^2 right? so you get ρ*cosθ/ρ^2 the ρ cancels out with one from ρ^2 so it's the limit as ρ goes to 0 of cosθ/ρ for any θ between [0, 2π) but 1/ρ tends to infinity and cosθ oscilates so the limit doesn't exist, although that one is easier just to do the iterateted limits one is 0 and the other inifinte so the limit doesn't exist.

[ad2894]

well in that case you cant prove there's a limit approaching from the x axis.

[ad2894]

then the limit doesnt exist

[Souliee]

As some people said!

More multivariable calculus to teh people!

p.s.

You're doing a great job, im a big fan. :)

d.s.

[proleyend]

Hi Patrick, are all of your new videos uploaded on your Math Tutoring Website? such as this one?

Cuz I love watching your videos, therefore, i mainly go to your website, which has them in order.

Thanks for your Videos, They are great and keep it up!

[patrickJMT]

i actually need to update my website! most of the videos are there with links, but some of my newer vids do not have links yet! but they will sooN!

[kcbanner]

You should do some triple integrals, or maybe multivariate taylor series :D

[HLSDK]

Rofl, KCBANNER, I see you're on my youtubes, watchin sum math vids!

[kcbanner]

Well yes I am this is why I'm not on Victor anymore, haha, school almost over!

[kcbanner]

This is great. Calc 2 final in a few days this is great review.

[babygirl31011]

this is great

[pitecman]

GReat VIDEOs mAN

[patrickJMT]

wow i sound terribly 'nasally' in this video... : )

[Btelgeuse]

Hahahaha, that doesn't matter ;)