\title{Monotonía II}
\language{en}
\range{-3..3}
\author{Gang XIAO}
\email{xiao@unice.fr}
\computeanswer{yes}
\format{html}
\precision{10000}

\text{no=no}
\text{Inf=inf}
\text{inc=siempre creciente}
\text{dec=siempre decreciente}
\text{pinc=creciente a partir de algún valor}
\text{pdec=decreciente a partir de algún valor}
\text{incdec=indeterminado hacia el infinito}
\text{growth=\incdec,\inc,\dec,\pinc,\pdec}
\integer{c1=random(2..10)*random(-1,1)}
\integer{c2=random(2..10)*random(-1,1)}
\integer{c3=random(2..10)*random(-1,1)}
\integer{c4=random(2..10)*random(-1,1)}
\integer{c5=random(2..10)*random(-1,1)}
\integer{C1=random(2..10)}
\integer{C2=random(2..10)}
\integer{C3=random(2..10)}
\integer{C4=random(2..10)}
\integer{C5=random(2..10)}
\integer{C10=random(5..15)}
\integer{CC1=random(10..100)}
\integer{C345=random(3,4,5)}
\real{d1=(randint(10..90)/100+randint(0..5))*random(-1,1)}
\real{d2=(randint(10..90)/100+randint(0..5))*random(-1,1)}
\real{s1=randint(1..20)/50+1}
\real{s2=randint(1..20)/50+1}
\integer{st=random(1..10)}
# terme,			debut, croiss,  inf,sup,min,max
\matrix{data=
\C1*n/(n^2+\CC1),		0, \pdec,	0,diff,0,same
\C1*n/(n^2+\CC1),		1, \pdec,	0,diff,\no,same
-\C1*n/(n^2+\CC1),		0, \pinc,	diff,0,same,0
-\C1*n/(n^2+\CC1),		1, \pinc,	diff,0,same,\no
\C1*cos(random(2,4)*pi*n)/random(n,n^2,n^3),random(1,2,3),\dec, 0,start,\no,same
-\C1*cos(random(2,4)*pi*n)/random(n,n^2,n^3),random(1,2,3),\inc, start,0,same,\no
\C1*cos(pi*n/2)/(n+\C2),	0, \incdec,	-\C1/(2+\C2),\C1/\C2,same,same
-\C1*cos(pi*n/2)/(n+\C2),	0, \incdec,	-\C1/\C2,\C1/(2+\C2),same,same
\C1*sin(pi*n/2)/(n+\C2),	0, \incdec,	-\C1/(3+\C2),\C1/(1+\C2),same,same
-\C1*sin(pi*n/2)/(n+\C2),	0, \incdec,	-\C1/(1+\C2),\C1/(3+\C2),same,same
\C10*ln(randint(5..15)*n+\C345)-n, randint(0..2),\pdec, -\Inf,diff,\no,same
-\C10*ln(randint(5..15)*n+\C345)+n, randint(0..2),\pinc, diff,\Inf,same,\no

}
\text{line=randomrow(\data)}
#text{line=row(rows(\data),\data)}
\text{uu=item(1,\line)}
\text{un=texmath(\uu)}
\integer{start=item(2,\line)}
\text{goodcr=item(3,\line)}
\text{inf=item(4,\line)}
\text{sup=item(5,\line)}
\text{inf=\inf notwordof start diff?pari(\inf)}
\text{sup=\sup notwordof start diff?pari(\sup)}
\real{inf=start iswordof \inf?evalue(\uu,n=\start)}
\real{sup=start iswordof \sup?evalue(\uu,n=\start)}
\text{infd=diff iswordof \inf?diff(\uu,n)}
\text{infe=diff iswordof \inf?solve(\infd,n=\start..100)}
\real{inf=diff iswordof \inf?
min(evalue(\uu,n=floor(\infe)),evalue(\uu,n=ceil(\infe)))
}
\text{supd=diff iswordof \sup?diff(\uu,n)}
\text{supe=diff iswordof \sup?solve(\supd,n=\start..100)}
\real{sup=diff iswordof \sup?
max(evalue(\uu,n=floor(\supe)),evalue(\uu,n=ceil(\supe)))
}

\text{min=item(6,\line)}
\text{max=item(7,\line)}
\text{min=\min iswordof same?\inf}
\text{max=\max iswordof same?\sup}

\statement{Estudiar el crecimiento, sup, inf, min, max de la sucesión
(<i>u<sub>n</sub></i>) para <i>n</i> \ge \start, donde
<p><center>
\( u_n = \un \relax ) .
</center> <p>
Escribir <tt>\no</tt> para indicar que determinado valor no existe, y
<tt>\Inf</tt> o <tt>-\Inf</tt> para +\infty o -\infty.
}

\choice{El crecimiento de la sucesión}{\goodcr}{\growth}
\answer{inf{<i>u<sub>n</sub></i>}}{\inf,\no,\Inf}{type=function}
\answer{sup{<i>u<sub>n</sub></i>}}{\sup,\no,\Inf}{type=function}
\answer{min{<i>u<sub>n</sub></i>}}{\min,\no,\Inf}{type=function}
\answer{max{<i>u<sub>n</sub></i>}}{\max,\no,\Inf}{type=function}
