MHB Evaluating limit of 2 variable function

[tmt1]

I have

$$\lim_{{(x, y)}\to{(0, 0)}} \frac{x^4 - y^4}{x^4 + x^2y^2 + y^4}$$

If I evaluate the limit along the x-axis, I get

$$\lim_{{(x, y)}\to{(0, 0)}} \frac{x^4 - y^4}{x^4 + x^2y^2 + y^4}$$

which evaluates to $1$.

If I evaluate the limit along the y-axis, I get

$$\lim_{{y}\to{0}} \frac{ - y^4}{ y^4}$$

which evaluates to $-1$.

Since the 2 limits are different, then the limit does not exist. Is this correct?

 

[Opalg]

Yes. (Sun)