Answer
See explanation
Work Step by Step
$\lim\limits_{(x,y) \to (0,0)} \frac{x^2+xy^2}{x^4+y^2} \overset{y=mx, m \in \mathbb{R} \setminus \{0\}}{=} \lim\limits_{x \to 0} \frac{x^2+m^2x^3}{x^4+m^2x^2} = \lim\limits_{x \to 0} \frac{1+m^2x}{x^2+m^2} \overset{x \to 0}{=} \frac{1}{m^2}$.
When $m$ changes $\frac{1}{m^2}$ value differs.
