(*uniform convergence example*) 

Clear[x];
ξ  =  1;
n  =  3;
f[x_] := Sin[x]
taylor[f_, c_, n_] := Normal[Series[f[x], {x, c, n}]]
\(\(\(t1 = taylor[f, 0, n]\)\(
\)
    \)\)
Plot[{f[x], t1,  f[x]  +  ξ,  f[x]  -  ξ}, {x, -10, 
        10}, PlotRange -> {-2, 2},  
      PlotStyle  ->  { {},  RGBColor[0, 0, 1],  RGBColor[0, 1, 0],  
          RGBColor[0, 1, 0]}]