legend=Table[ToString["y=x"^i,TraditionalForm],{i,{1,2,3,10,100}}];
ListLinePlot[Table[{x,x^n},{n,{1,2,3,10,100}},{x,0,1,0.001}],PlotLegends->legend,AxesLabel->Automatic,PlotStyle->Thickness[0.005],LabelStyle->Directive[15,Bold,FontFamily->"Helvetica"]]

legend=Table[ToString[(x^2+1)+1/(x^2+1)^i,TraditionalForm],{i,{1,2,3,10}}];
ListLinePlot[Table[{x,x^2+1+1/(x^2+1)^n},{n,{1,2,3,10}},{x,1,2,0.001}],PlotLegends->legend,AxesLabel->Automatic,PlotStyle->Thickness[0.003],LabelStyle->Directive[15,Bold,FontFamily->"Times New Roman"]]

legend=Table[ToString[x^2/(x^2+i),TraditionalForm],{i,{1,3,10,50,1000}}];
ListLinePlot[Table[{x,x^2/(x^2+n)},{n,{1,3,10,50,1000}},{x,-10,10,0.001}],PlotLegends->legend,AxesLabel->Automatic,PlotStyle->Thickness[0.005],LabelStyle->Directive[15,Bold,FontFamily->"Times New Roman"]]

legend=Table[ToString@StringForm["n =  ``",i],{i,{1,2,3,10,40}}];
ListLinePlot[Table[{x,n*x*Exp[-n*x^2]},{n,{1,2,3,10,40}},{x,0,1,0.001}],PlotLegends->legend,AxesLabel->Automatic,PlotStyle->Thickness[0.005],LabelStyle->Directive[15,Bold,FontFamily->"Times New Roman"],PlotRange->All]

legend=Table[ToString[Sqrt[x^2+1/i],TraditionalForm],{i,{1,2,3,10,50}}];
A=ListLinePlot[Table[{x,Sqrt[x^2+1/n]},{n,{1,2,3,10,50}},{x,-2,2,0.001}],PlotLegends->legend,AxesLabel->Automatic,PlotStyle->Thickness[0.005],LabelStyle->Directive[15,Bold,FontFamily->"Times New Roman"],PlotRange->All];
B=Plot[Abs[x],{x,-2,2},AxesLabel->Automatic,PlotStyle->{Black,Thickness[0.005]},PlotRange->All];Show[A,B]

legend=Table[ToString[Sin[i*x]/i,TraditionalForm],{i,{1,2,3,10,50}}];
A=ListLinePlot[Table[{x,Sin[i*x]/i},{i,{1,2,3,10,50}},{x,-2,2,0.001}],PlotLegends->legend,AxesLabel->Automatic,PlotStyle->Thickness[0.005],LabelStyle->Directive[15,Bold,FontFamily->"Times New Roman"],PlotRange->All];
B=Plot[Cos[x],{x,-2,2},AxesLabel->Automatic,PlotStyle->{Black,Thickness[0.005]},PlotRange->All];Show[A,B]