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{\bf Quiz \#6; Tuesday, date: 02/27/2018}
{\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 Find the limit, if it exists, or show that the limit does not exist.
\[
\lim_{(x, y) \to (0, 0)} \frac{xy^3}{x^2 + y^6}
\]
\item {\em True / False?} If $f$ is a function whose domain contains points arbitrarily close to $(2, 3)$, then
\[
\lim_{(x, y) \to (2, 3)} f(x, y) = (2, 3).
\]
\item {\em True / False?} Consider two functions $f$ and $g$ that are both defined on the domain of $f$. Suppose the domain of $f$, $D_f$ is contained in the domain of $g$, $D_g$ (i.e.\ $D_f$ is a subset of $D_g$) and $f(x) = g(x)$ for any points $x$ in $D_f$. If the origin is in $D_f$ and $f$ is continuous at the origin, then $g$ is also continuous at the origin.
\end{enumerate}
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