[Steps Shown] Consider the function f: R^2 \rightarrow R given by f(x, y)= \begincases(x^2(y-1))/(√x^2+(y-1)^2), (x, y) ≠q(0,1) , 0, (x, y)=(0,1)\endcases

Question: Consider the function $f: \mathbb{R}^{2} \rightarrow \mathbb{R}$ given by

\[f(x, y)= \begin{cases}\frac{x^{2}(y-1)}{\sqrt{x^{2}+(y-1)^{2}}}, & (x, y) \neq(0,1) \\ 0, & (x, y)=(0,1)\end{cases}\]

Is $f$ continuous at the point $(0,1)$ ?
Find $\partial f / \partial x(0,1)$ and $\partial f / \partial y(0,1)$.

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[Steps Shown] Consider the function f: R^2 \rightarrow R given by f(x, y)= \begincases(x^2(y-1))/(√x^2+(y-1)^2), (x, y) ≠q(0,1) , 0, (x, y)=(0,1)\endcases

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