Manipulate[Plot[(a*x^2+x+1)/(x^2+x+1),{x,0,100},PlotStyle->Blue,PlotRange->{{0,100},{0,6}},Epilog->{Text["(lim_(x -> ∞))",{10,1}],Text[((a (x^2)+x+1)/((x^2)+x+1)),{20,1}],Text["(Overscript[=, ∞/∞])",{30,1}],Text[a,{35,1}]}],{a,2,6,1}]