O15-C077

> restart;with(plots);with(student):
> 

  [animate, animate3d, animatecurve, changecoords, complexplot,

        complexplot3d, conformal, contourplot, contourplot3d,

        coordplot, coordplot3d, cylinderplot, densityplot, display,

        display3d, fieldplot, fieldplot3d, gradplot, gradplot3d,

        implicitplot, implicitplot3d, inequal, listcontplot,

        listcontplot3d, listdensityplot, listplot, listplot3d,

        loglogplot, logplot, matrixplot, odeplot, pareto, pointplot,

        pointplot3d, polarplot, polygonplot, polygonplot3d,

        polyhedra_supported, polyhedraplot, replot, rootlocus,

        semilogplot, setoptions, setoptions3d, spacecurve,

        sparsematrixplot, sphereplot, surfdata, textplot, textplot3d,

        tubeplot]

> f:=x*y/(x+y);

                                    x y
                              f := -----
                                   x + y

> plot3d(f,x=0..1,y=0..1);

> value(Doubleint(f,x=0..1,y=0..1));

                                 2
                          2     x        2
                     x + x  ln(-----) - x  ln(x)
                               x + 1

> for n from 1 to 60 do S[n]:=sum(sum(p*q/(p+q),q=1..2*n),p=1..2*n)/8/n^3 od:[seq(evalf(S[n]),n=1..30)];
> 

  [.3541666667, .2801339286, .2551650767, .2426073276, .2350460196,

        .2299932006, .2263779083, .2236629695, .2215492424,

        .2198569069, .2184713598, .2173161043, .2163381265,

        .2154995255, .2147724865, .2141361347, .2135744975,

        .2130751455, .2126282617, .2122259889, .2118619646,

        .2115309811, .2112287351, .2109516396, .2106966806,

        .2104613073, .2102433464, .2100409344, .2098524650,

        .2096765453]