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{\bf Quiz \#2; Tuesday, date: 01/30/2018}
{\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 an equation of the sphere that passes through the origin and whose center is $(1, -2, 2)$.
\item {\em True / False?} Suppose $f$ and $g$ are functions of $t$, then the following two parametric curves has the same tangent line at $t = 0$:
\[
x = f(t), ~~~~ y = g(t);
\]
and
\[
x = f(-2t), ~~~~ y = g(-2t).
\]
\item {\em True / False?} Given a polar curve $r = f(\theta)$, the area under the curve and above the $x$-axis from $\theta = \alpha$ to $\theta = \beta$ is always given by
\[
\int_\alpha^\beta \frac{1}{2} f(\theta)^2 \,d\theta.
\]
\end{enumerate}
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