ClearAll;
$DefaultFont = {"Times-Roman",10};
Needs["Graphics`Graphics`"];

xticks = {a1, 0.25(3a1 + b1), 0.5(a1+b1), 0.25(a1 + 3b1), b1};
yticks = {a2, 0.25(3a2 + b2), 0.5(a2+b2), 0.25(a2 + 3b2), b2};
a1 = 0; b1 = 8; a2 = 0; b2 = 2;
axesorigin = {1.01a1-0.01b1,1.01a2-0.01b2};
plotrange = {{a1,b1},{a2,b2}};
s[0,x] = 1;
s[n_,x_]:= Together[(s[n-1,x] + x/(s[n-1,x])^2)/2];
plotsq:= Plot[x^(1/3),{x,a1,b1},
			PlotStyle -> Dashing[{0.01,0.01}]];
plot[n_]:= Plot[Evaluate[s[n,x]],{x,a1,b1},
			    Ticks -> {xticks, yticks}];
a11:= Show[plot[0],plotsq, AxesOrigin -> axesorigin, Axes->True,
		   PlotLabel -> "n = 0", AxesLabel -> {"x","y"},
		   Ticks->{xticks,yticks},
		   PlotRange -> plotrange];
a12:= Show[plot[1],plotsq, AxesOrigin -> axesorigin, Axes->True,
		   PlotLabel -> "n = 1", AxesLabel -> {"x","y"},
		   Ticks->{xticks,yticks},
		   PlotRange -> plotrange];
a21:= Show[plot[2],plotsq, AxesOrigin -> axesorigin, Axes->True,
		   PlotLabel -> "n = 2", AxesLabel -> {"x","y"},
		   Ticks->{xticks,yticks},
		   PlotRange -> plotrange];
a22:= Show[plot[3],plotsq, AxesOrigin -> axesorigin, Axes->True,
		   PlotLabel -> "n = 3", AxesLabel -> {"x","y"},
		   Ticks->{xticks,yticks},
		   PlotRange -> plotrange];
a31:= Show[plot[4],plotsq, AxesOrigin -> axesorigin, Axes->True,
		   PlotLabel -> "n = 4", AxesLabel -> {"x","y"},
		   Ticks->{xticks,yticks},
		   PlotRange -> plotrange];
a32:= Show[plot[5],plotsq, AxesOrigin -> axesorigin, Axes->True,
		   PlotLabel -> "n = 5", AxesLabel -> {"x","y"},
		   Ticks->{xticks,yticks},
		   PlotRange -> plotrange];
Show[GraphicsArray[{{a11,a12},{a21,a22},{a31,a32}}],
		PlotLabel->"                          Figure E4.5\n\n
		     Oscillatory convergence of cube root function sequence"]