Limits of Functions of Two Variables

[aegurak]

Hey this video was fantastic! I'm taking multivariable calculus for the first time and my professor has the worst possible teaching methods so I really appreciate this!

[seth-langendoen]

very helpful. It took me a while to find a video that explaned paths as opposed to basic algebra tricks that only work for some functions.

[hohner]

when my lecturer tried to explaain these, he bored us to absolute death and made it look like a horrible endless thing to figure out, yet this was simmple to understand, and didnt take half as long to explain. there should just be a youtube college run by you guys lol

[Mathispoweru]

@leemonastesse84 It is x^2 + x^2 = 2x^2. The path is y = -x, so y^2 = (-x)^2 = x^2. The denominator along the path would be x^2 + x^2 = 2x^2. Notice the numerator is xy = x(-x) = -x^2. Hope that helps.

[DauntedMelodies]

This is the only thing I was having trouble with. Midterm in about 5 hours. You're a saint!

[mohamedhamdy]

Thank you for doing non lim (x, y) -> (0, 0) problems! Very helpful.

[Mathispoweru]

The second example does how a limit that DNE. If you have a suggested example, I would definitely consider adding it.

[diamondz]

I don't get how you know which paths to take...

[stevenhamilton]

In your second example you said as the path y=-x the denominator is x^2+(-x^2)= 2x^2

How is that possible if you're adding a negative, that makes no sense. They should be zero right?

[macmos]

in finding the limit of a function when you replace f(x, y) can you use any function? My assumption is that you can. can you replace y, for example, with x^3 or sqrt(x) or any other arbitrary function. Or does it have to be in the domain of f(x, y). If so, how would you know which function to use for approaching the limit?

[leemonastesse]

How does the denominator equal (2x^2) at the 7:25 mark. I see a x^2 - x^2. Can someone tell me if this is me or the video that made the mistake. Thank You!

[gorrelaakhil]

Excellent great source in corona pandemic.

[AhmedKMoustafa]

great slides , it was helpful, but I hope you make a second advanced video for those who want more, it can contain nice paths like : y=mx, that detemines if the function D.N.E as it is dependent on mx,
It would be great also, if the second video covers some trig functions
Best Regards

[mohamedhamdy]

great slides , it was helpful, but I hope you make a second advanced video for those who want more, it can contain nice paths like : y=mx, that detemines if the function D.N.E as it is dependent on mx,
It would be great also, if the second video covers some trig functions
Best Regards

[jorijgijrgij]

I agree. If you approach it from y = x, the value of the limit become 0.5 which would suggest that the limit does not exist at this point.

[OscarFernandez]

You explain this very nice, the graph is very necessary, anyone know what software can make this functions plots ?

[nishantcharas]

why are you choosing only y=x or -x while other paths are also possible like y=x^2 and many more????

[sksoh]

@ 8:27 without graphing tools how would you know if the graph is continuous at (4, 2)

[yuhaooo]

although y=x passes through that point, it is jus a line parallel to x-y plane.... how can prove the limit??

[SlapMarket]

3:00
Did you point out the coordinate (1, 1, 1)? I thought (x, y) was 2D, on the xy plane. Why did you go into space for the point (1, 1)?