\( (*\ 
      This\ example\ generates\ the\ data\ to\ help\ students\ understand\ epilson - delta\ \(\(proofs\)\(.\)\)\ *) 


    f[x_]\  := 3  x - 5\)
ξ  =  1/2;
l  =  1;
c  =  2;
y  =  l  +  ξ;
z  =  l  -  ξ;
Plot[{f[x],  y, z},  {x, -5, 
        5}, 
PlotRange -> {-4, 
          4},  
PlotStyle  ->  { RGBColor[0, 0, 1],  
          RGBColor[0, 1, 0],  RGBColor[0, 1, 0]}]
NSolve[f[x]  ==  y]
\(\(\(NSolve[f[x]\  == \ z]\)\(
\)
    \)\)
newtable  =  
        Table[{x,   N[Abs[x - c]],  N[Abs[f[x]  -  l]]},  {x, 1.5, 
            2.5,  0.1}];
\(TableForm[newtable, \ TableDirections\  -> \ {Column, \ Row}, 
	
      TableHeadings\  -> \ {None, \ {\ "x", \ "|x - c|", \ "|f[x] - L|"}}, 
	TableSpacing\  -> \ {3, 3}]\)