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

\integer{a=random(2..10)}
\integer{A=random(2..10)*random(-1,1)}
\integer{b=random(11,13,17,19)}
\text{rat=random(1/3,2/3,1/4,3/4,1/5,2/5,3/5,4/5)}
\text{pm=random(+,-)}
\text{flist=	\b/(\a\pm x),
		sqrt(\a\pm x),
		atan(\a\pm x),
		sin(\A\pm x),
		cos(\A\pm x),
		(\a\pm x)^(\rat)
		}
\integer{cnt=items(\flist)}
\integer{ch=random(1..\cnt)}
\function{f=item(\ch, \flist)}
\integer{u1=random(1..9)}
\integer{u1=\u1=\a?\a-1}
\text{u2=item(\ch,	{\b \over {\a \pm \u1}},
			\sqrt{\a \pm \u1},
			\arctan\left(\a \pm \u1\right),
			\sin\left(\A \pm \u1\right),
			\cos\left(\A \pm \u1\right),
			\left(\a \pm \u1 \right)^{\rat}
			)}
\text{u3=item(\ch,	{\b \over {\a \pm \u2}},
			\sqrt{\a \pm \u2},
			\arctan\left(\a \pm \u2\right),
			\sin\left(\A \pm \u2\right),
			\cos\left(\A \pm \u2\right),
			\left(\a \pm \u2 \right)^{\rat}
			)}
\text{u4=item(\ch,	{\b \over {\a \pm \u3}},
			\sqrt{\a \pm \u3},
			\arctan\left(\a \pm \u3\right),
			\sin\left(\A \pm \u3\right),
			\cos\left(\A \pm \u3\right),
			\left(\a \pm \u3 \right)^{\rat}
			)}

\statement{La sucesión \((u_n)) tal que
 <center>\( u_1=\u1\;,\;u_2=\u2\;, )</center>
 <center>\( u_3=\u3\;, )</center>
 <center>\( u_4=\u4\;,\; \cdots )</center>
es una sucesión recursiva definida por 
\(u_{n+1}=f\left(u_n\right)) para cierta función \(f). Encontrar dicha funcion.
}

\answer{f(x)}{\f}{type=default}
