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{\bf Quiz \#7; Tuesday, date: 03/06/2018}
{\bf MATH 53 Multivariable Calculus with Stankova}
{\bf Section \#114; time: 2 -- 3:30 pm}
{\bf GSI name: Kenneth Hung}
{\bf Student name:}
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\begin{enumerate}
\item Use the Chain Rule to find the indicated partial derivatives.
\[
T = \frac{v}{u + 2v}, ~~~~ u = pq \sqrt{r}, ~~~~ v = p \sqrt{q} r;
\]
Find $\partial T / \partial p$, $\partial T / \partial q$, $\partial T / \partial r$ when $p = 1, q = 1, r = 4$.
\item {\em True / False?} There exists a function not differentiable at the origin that is continuous at the origin and has partial derivatives at the origin.
\item {\em True / False?} Suppose $g(x, y)$ is a linear function and $f(x, y)$ is a two-variable function, not necessarily linear. If
\[
f(0, 0) = g(0, 0) ~~~~ \text{ and } ~~~~ \lim_{(x, y) \to (0, 0)} |f(x, y) - g(x, y)| \to 0
\]
then $g$ is a good linear approximation to $f$, so $f$ is a differentiable function.
\end{enumerate}
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