\documentclass[12pt]{amsart}

\usepackage{graphics}

\setlength{\textwidth}{6.5in}
\setlength{\hoffset}{-.75in}

\setlength{\parindent}{0pt}
\everymath={\displaystyle}
\pagestyle{empty}

\newcommand{\N}{\ensuremath{\mathbb{N}}}

\begin{document}

\thispagestyle{empty}

\textbf{Math 366: Honors Analysis II}
\hfill\makebox[2.5in][r]{Name:\hrulefill}

\textbf{Quiz 2}\quad \textsl{February 16, 2001}

\bigskip
1. Define:

a) $\mathcal{F}$ is uniformly equicontinuous.

\vfill

b) $f*g$

\vfill

2. State:

a) The Weierstrass Approximation Theorem

\vfill

b) The Arzela-Ascoli Theorem.

\vfill

3. Calculate the radius of convergence of the series $\sum_{n=0}^\infty (1
+ (-1)^n + 1/n)^n x^n$.

\vfill

\newpage
Prove two of the following:

4.  Suppose $f$ is integrable and has compact support. If $g$ is a
polynomial of degree $n$ then $f*g$ is a polynomial of degree $\le n$.

\vfill
 
5. Suppose $f\in C[0,1]$ and $\int_0^1 f(x) x^n dx = 0$ for all $n\in \N$.
Then $f(x) = 0$ for all $x\in[0,1]$. (Hint: Use the Weierstrass
Approximation Theorem.)

\vfill

6.  If $f_n\in C^1[a,b]$ and $|f_n'(x)|\le M$ for all $n\in \N$, then
$\{f_n\}$ is equicontinuous.

\vfill

\end{document}
