(* :Author: Christopher Moretti *) 
(* :Summary: InfinityPlot[function,t,n] creates a plot used to aid the detection of limits of -
function- in the variable t.  n is the number
of PlotPoints used (and should be >40 or so) *) 
(* :History: Version 1.0 by Christopher Moretti, 1997 *) 
 
InfinityPlot[f_,t_,n_]:= 
 Block[{g,x,p}, 
  g= f/. t->Tan[x]; 
  p=Plot[ArcTan[g],{x,-Pi/2+.001,Pi/2-.001},AspectRatio->Automatic, 
        PlotRange->{-Pi/2,Pi/2},PlotPoints->n,DisplayFunction->Identity]; 
  Show[p,Graphics[Line[{ {-Pi/2,-Pi/2},{-Pi/2,Pi/2}}]], 
   Graphics[Line[ { {-Pi/2,Pi/2},{Pi/2,Pi/2}}]], 
   Graphics[Line[ { {Pi/2,Pi/2},{Pi/2,-Pi/2}}]], 
   Graphics[Line[ { {Pi/2,-Pi/2},{-Pi/2,-Pi/2}}]], 
   DisplayFunction->$DisplayFunction] 
 ];