Multivariable Calculus Limit of x^2y/(x^2 + y^2) using Polar Coordinates

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Our stupid teacher gave this to us and said prove that it doesn't exist.
I was trying for almost a day

lehninger

Can we solve the problem if we have in x^2-y^2 ?

sultanalajmi

Where did you get this question from ? Any book or Online resource ?

Anya-wlyw

found this in the middle of my test ty so much

viniciush.

why do you absolute rcos^2xsinx at the end? x=theta

benbadenhorst

isnt this solution inappropriate
here you have assumed that x and y lie on a circle with radius r which is not true

sarthakchoudhary

Other than polar coordinates can you help me with by substituting y equal to x or minus x or 2x.
Plz sir
Btw very informative video
Thankyou 🙏

cuber-singh

Oh i have finally arrived to the place in the internet where someone explains actual exam limits and not just the ones that can be solved making y=0 or x=0.
Thank you sir

facundo_

is this really enough to show continuity? we might approach (0, 0) in a way other than a straight line

justwest

what if you had x*sin(y) in the numerator instead? I'm not sure how I'd solve the sin(r sin theta) part after plugging it in.

Edigor

The video sound is pretty good, beyond my imagination

hatrinh

How will we prove its not difderentiable

AKytub

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