Compute the limit of the multivariable function

[granite granite]

I need to know how to explain this problem. I knew that the answer is 0 but I dont know how to prove it (or maybe im wrong). Pls help me.

[tardy flicker]

Converting to polar is always helpful

[granite granite]

How to convert it to polar ?

I mean, I didn't know that I can convert a multivariable function to polar

Can you show me how to convert it 😭

[compact lance]

do you not just consider one limit at a time?

choose one variable to -> 0

[tardy flicker]

no

[compact lance]

f then simplifies to xx or yy/2 where variable approach 0

[tardy flicker]

multivariable limits must consider _every_path

[granite granite]

So ... how do you do that problem ;-;

I still dont know how to compute

[tardy flicker]

Try $x=r\cos\theta$ and $y=\frac{r}{\sqrt2}\sin\theta$

[robust pier]

SWR

[granite granite]

Let me try