\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} The function $S$ (the ``squaring
function'') has domain all real numbers and is defined by the formula
$S(x)=x^2$ for all $x$.

\smallskip

\noindent a) Consider the function $T$ whose domain is also all real
numbers which is defined by
$$ T(x)= \cases{ S(x) & if $x \ne 3$\cr
                7 & if $x=3$\cr}\,. $$

\noindent Sketch a graph of $T$. What is ${\lim\limits_{x\to 5}
T(x)}$?  What is ${\lim\limits_{x\to 3} T(x)}$? Support your
assertions.

\medskip

\noindent b) An evil interstellar visitor {\it changes} exactly {\it
one million values} of $S$ and creates a new function, $V$. What can
be said about ${\lim\limits_{x \to a} V(x)}$ for all values of $a$?
Support your assertions.









\vfil\eject\end