
title=2. Producto mixto
sol=2
prompt=$m_g(x)

sh_=!randint 1,4
!ifval abs($z0)=$sh_
 sh_=$[abs($z0)+1]
!endif
coe=!randint 1,4

T0=!randitem -9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9
t1=!randitem -9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9
t2=!randitem -9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9
t3=!randitem -9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9

poly1=!rawmath $t2*x^2+$t1*x+$T0
poly2=!rawmath $t3*x^3+$poly1

!ifval $z0!=0
 pol1=!mathsubst x=(x+$z0) in $poly1
 pol2=!mathsubst x=(x+$z0) in $poly2
!else
 pol1=$poly1
 pol2=$poly2
!endif

flist=sin($coe*x),cos($coe*x),exp($coe*x),log(x+1),($pol1),($pol2)
!ifval $z0=0
 Flist=$flist
!else
 Flist=sin($coe*x-$[$coe*$z0]),cos($coe*x-$[$coe*$z0]),exp($coe*x-$[$coe*$z0]),\
   log(x+$[1-$z0]),($poly1),($poly2)
!endif
n_=!itemcnt $flist
n_=!randint 1,$n_
exp=!item $n_ of $flist
Exp=!item $n_ of $Flist
explicite=!htmlmath $Exp

parisrc=ser3=Ser($exp,x); ser2=ser1 * ser3 + O(x^$[$order+1]); poly2=Pol(ser2);

given=ser1
calcname=<p><center>$m_g(x) = $explicite&nbsp;$m_f(x)&nbsp;.</center> <p>

