Calculus 3 Problem - Multivariate Limit

[PasserbyLance]

This problem has been putting me in a lot of dead ends.

It goes as follows:
find the limit for (x,y)->(0,0), the function:

the problem requires you to use the squeeze theorem and absolute value theorem to find the limit without polar coordinate substitution.
i've tried different ways of framing the fraction but alas no hope, is anyone able to help?
this is what i did:

 

[Steven G]

Can you know apply the squeeze theorem and see what you get?

 

[PasserbyLance]

Can you know apply the squeeze theorem and see what you get?

well the limit of square root of x when (x,y)->(0,0) is 0 so it would seem that the squeeze theorem worked, but i need some verification

 

[dunkelheit]

Correct. The point is that since [MATH]\sqrt{x}[/MATH] is independent of [MATH]y[/MATH] and its limit is [MATH]0[/MATH] as [MATH]x \to 0^+[/MATH], you can conclude that, for the squeeze theorem, your limit in two variables is [MATH]0[/MATH] as well (remember that limits of 2 or more variables can be insidious because you have to prove that the limit is independent from the direction you use to approach the point; in this case the point is the origin).