Plot[{Abs[Sin[x]/(1 + x (((Sin[x]))^2))], (10/x)}, {x, 1, 1050}, 
      PlotRange -> {-1, 1}, 
      PlotStyle -> {Red, Blue}]

Plot[{Abs[Log[(((1 + (1/x)))^x)] - 1], (1/x)}, {x, 1, 105}, 
      PlotRange -> {-1, 1}, 
      PlotStyle -> {Red, Blue}]

Plot[{Abs[Log[(((1 + (1/x)))^x)] - 1], (1/x)}, {x, 1000, 1050}, 
      PlotRange -> {- .0001, 0.001}, 
      PlotStyle -> {Red, Blue}]

Plot[{Log[(((1 + (1/x)))^x)], 1}, {x, 1, 10}, 
      PlotRange -> {- .0001, 2}, 
      PlotStyle -> {Red, Blue}]