[See Solution] Consider the function f: R^3 \rightarrow R given by f(x, y, z)= \begincases(x y z)/(√x^2+y^2+z^2), (x, y, z) ≠q(0,0,0) , 0, (x,

Question: Consider the function $f: \mathbb{R}^{3} \rightarrow \mathbb{R}$ given by

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

Is $f$ continuous at the point $(0,0,0)$ ?
Find $\partial f / \partial x(0,0,0), \partial f / \partial y(0,0,0)$ and $\partial f / \partial z(0,0,0)$.
Find the directional derivative of $f$ at $(0,0,0)$ in an arbitrary direction $\mathrm{v}=\left(v_{1}, v_{2}, v_{3}\right)$.

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Coefficient of Determination Calculator - MathCracker.com

[See Solution] Consider the function f: R^3 \rightarrow R given by f(x, y, z)= \begincases(x y z)/(√x^2+y^2+z^2), (x, y, z) ≠q(0,0,0) , 0, (x,

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