Answer
Limit does not exist.
Work Step by Step
Consider $f(x,y)=-\dfrac{x}{\sqrt{x^2+y^2}}$
Let us consider the approach: $(x,y) \to (0,0)$ along $y=mx$
Then, we get $\lim\limits_{(x,y) \to (0,0)}-\dfrac{x}{\sqrt{x^2+(mx)^2}}=\lim\limits_{(x,y) \to (0,0)}-\dfrac{1}{\sqrt{1+m^2}}$
This shows that there are multiple limit values and thus the limit does not exist at the point $(0,0)$ for the given function.