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

\text{if=<i>f</i>}
\text{BR=<b>R</b>}
\text{tany=any}

\integer{n2=random(1..4)*2}
\integer{n1=\n2+1}
\integer{c=random(1..9)}
\integer{oe=random(1,2)}
\integer{n=item(\oe,\n1,\n2)}
\integer{m=\n-1}
\text{sn=<sup>\n</sup>}
\text{s2=<sup>2</sup>}

\text{flist=|x\sn|-\c, (|x|)\sn-\c, |x\sn-\c|, |(x-\c)\sn|, (|x-\c|)\sn,
	|x(x-\c)\sn|, |x\sn(x-\c)|, |x\s2(x-\c)\sn|, |x\sn(x-\c)\s2|, |x-\c|(x-\c)\sn
}
\integer{take=random(1..items(\flist))}
\text{f=item(\take,\flist)}
\text{order=\oe=1?item(\take,\m,\m,0,\m,\m,	0,0,\m,\m,\n)}
\text{order=\oe=2?item(\take,\tany,\tany,0,\tany,\tany,	  0,0,\tany,\tany,\n)}

\statement{Let \if: \BR -> \BR be the function defined by
\if(x)&nbsp;=&nbsp;\f. What is the order of differentiability of \if&nbsp;?
<p>
<b>Instructions/Examples.</b><ul>
<li>Type <tt>3</tt> if \if is differentiable to order 3 but not to order 4.
<li>Type <tt>0</tt> if \if is continuous but not differentiable.
<li>Type <tt>-1</tt> if \if is not continuous.
<li>Type <tt>\tany</tt> if \if is differentiable to any order.
</ul>
}

\answer{Order of differentiability}{\order}

