Manipulate[Plot[(1+a/x)^x,{x,0,100},PlotStyle->Blue,PlotRange->{{0,100},{0,Exp[5]}},Ticks->{Automatic,Table[Exp[i],{i,0,5}]},Epilog->{Text["\!\(\*UnderscriptBox[\(lim\), \(x -> \\ ∞\)]\)",{10,Exp[4.75]}],Text[(((1+(a/x)))^x),{20,Exp[4.75]}],Text["(Overscript[=, (1^∞)])",{30,Exp[4.75]}],Text[e^a,{35,Exp[4.75]}]}],{a,1,5,1}]