\title{Continuity and sequences}
\language{en}
\range{-0.9..0.9}
\author{Gang XIAO}
\email{xiao@unice.fr}
\computeanswer{yes}
\format{html}
\precision{10000}

\integer{center=random(-9..9)}
\text{tyes=Yes}
\text{tno=No}
\text{if=<i>f</i>}
\text{in=<i>n</i>}
\text{xn=x<sub>\in</sub>}
\text{BR=<b>R</b>}
\text{ne=<sup><img src=\imagedir/ne.gif align=middle></sup>}
\text{infty=<img src=\imagedir/infty.gif>}
\text{lim=lim<sub>\in->\infty</sub>}
\text{cont=is continuous}
\text{noncont=is not continuous}
\text{exist=there exists a sequence}
\text{forall=for all sequences}
\text{tq=such that}
\text{cv=convergent}
\text{dv=divergent}
\text{goodlim=\cv with \lim\if(\xn)&nbsp;=&nbsp;\if(\center)}
\text{badlim=\cv but \lim\if(\xn)&nbsp;\ne&nbsp;\if(\center)}

\integer{r=random(1..8)}
\integer{rr=random(1,2)}
\text{v1=\r<=4?\cont:\noncont}
\text{v2=\r%2=0?\forall:\exist}
\text{v3=\r%2=0?:\tq}
\text{v4=item(floor((\r+1)/2),\cv,\goodlim,\dv,\badlim)}
\text{vfunc=\if \v1 on \center}
\text{ceq=\rr=1?:\xn \ne \center and}
\text{vseq=\v2 (\xn) with \ceq \lim \xn = \center, \v3 the
sequence (\if(\xn)) is \v4}

\text{gooda=\rr=1?item(\r,\tyes,\tyes,\tyes,\tyes, \tyes,\tno,\tno,\tno):
		  item(\r,\tyes,\tyes,\tyes,\tyes, \tno,\tno,\tno,\tno)}
\text{goodb=\rr=1?item(\r,\tno,\tyes,\tno,\tyes,   \tyes,\tyes,\tyes,\tyes):
		  item(\r,\tno,\tno,\tno,\tyes,    \tyes,\tyes,\tyes,\tyes)}

\statement{Let \if: \BR -> \BR be a real function. Are the following
statements justified?
<p>
A. If \vfunc, then \vseq.
<p>
B. If \vseq, then \vfunc.
}

\choice{Statement A}{\gooda}{\tyes,\tno}
\choice{Statement B}{\goodb}{\tyes,\tno}

