Answer
The limit does not exist
Work Step by Step
Consider $f(x,y)=\dfrac{x^4-y^2}{x^4+y^2}$
Let us consider the approach: $(x,y) \to (0,0)$ along $y=kx^2$
Then, we get $\lim\limits_{x \to 0}\dfrac{x^4-(kx)^2}{x^4+(kx)^2}=\lim\limits_{x \to 0}\dfrac{1-k^2}{1+k^2}=\dfrac{1-k^2}{1+k^2}$
This shows that there are multiple limit values and thus the limit does not exist at the point $(0,0)$ for the given function.
