\magnification = \magstep1
\nopagenumbers
\leftline{Mathematics 242 -- Principles of Analysis}
\leftline{Definitions Quiz 6 -- March 22, 2013}
\medskip
\leftline{Your Name: $\underline{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ }$}
\bigskip
\noindent
A) (5)  Give the $\varepsilon$, $\delta$ form of the definition of the statement 
``$f$ is continuous at $c$.''   
\vglue 4.0truein
\noindent
B) (5)  Let 
$$f(x) = \cases{0 & if $x < 0$ \cr
                1 & if $x \ge 0$.\cr}$$
What is $c = {\rm lub}\left(\left\{x \in {\bf R}\mid f(x) \le {1\over 2}\right\}\right)$.  Is $f(c) \le {1\over 2}$?  
\bye
