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[All Steps] Let f(x, y)=ll0 \text if y=x^2 , 1 \text if y ≠q x^2 Show that this has a limit at the origin along every polynomial path approaching the

Question: Let $f(x, y)=\left\{\begin{array}{ll}0 & \text { if } y=x^{2} \\ 1 & \text { if } y \neq x^{2}\end{array}\right.$ Show that this has a limit at the origin along every polynomial path approaching the origin and of the form $y=q(x)$, but that there is exactly one polynomial for which the limit differs from all of the others. So for each polynomial of the form $y=q(x)$ (with $q(0)=0$ ), compute $\lim _{x \rightarrow 0}(f(x, q(x))$

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[All Steps] Let f(x, y)=ll0 \text if y=x^2 , 1 \text if y ≠q x^2 Show that this has a limit at the origin along every polynomial path approaching the

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