Sample Quiz

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{\sc \Large Math 1820} \hfill \today \\
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Name: \underline{\hspace{2.0in}} \\
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This quiz covers the material from the text on the Theorem of
Pythagoras in section~1.1 and section~1.3.  Because we realize most
students suffer from fits of stupidity and are over all feebleminded,
we racap the theorem here:

\begin{thm}[Pythagoras]
If the sides of a right triangle are labeled $a$, $b$ and $c$ where
$c$ is the hypotenuese, then
\[
a^2 + b^2 = c^2.
\]
\end{thm}

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1.  Let $T$ denote a triangle with sides of length 3, 4 and 5.  Let $x \in
\R$ be an unknown quantity.
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\begin{enumerate}
\item[a)]Assume $T$ is a right triangle.  Explain which side must be
the hypotenuese by using the triangle inequality. \vspace{1.3in}

\item[b)]Explain how to use Pythagoras' Theorem to verify that $T$ is a
right traingle.\vspace{1.3in}

\item[c)]Suppose $S$ is a right triangle whose sides have lengths 4, 5,
and $x$.  Determine $x$. \vspace{1.3in}
\end{enumerate}

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2.  On the back of this sheet, compute $\displaystyle
\int_{-\infty}^\infty \frac{1 + \sin(x^3)}{1 + x^{12}} dx$.
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