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\textbf{Partial Differentiation}

\textit{\textbf{Functions of more than one variable}}
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\textbf{Question}

Describe the ``level hypersurfaces'' for the function
$$f(x,y,z,t)=x^2+y^2+z^2+t^2$$

\textbf{Answer}

The ``level-hypersurface'' $f(x,y,z,t)=c>0$ is the ``4-sphere'' of
radius $\sqrt{c}$ centred at the origin in $\bf{R}^4$. i.e. it consists
of all points in $\bf{R}^4$ at a distance $\sqrt{c}$ from the origin.

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