PROBLEM 48:
  The following cells will help you visualize the setup.

Clear[F,x,y,z,one];
F[x_,y_,z_]=(x^2)+(z^2)-1;
one=ContourPlot3D[F[x,y,z]==0,{x,-1,1},{y,-1,1},{z,-1,1},PlotPoints->5,Axes->True,ViewPoint->{30,10,5},AxesLabel->{x,y,z}];
Clear[F,x,y,z,other];
F[x_,y_,z_]=(y^2)+(z^2)-1;
other=ContourPlot3D[F[x,y,z]==0,{x,-1,1},{y,-1,1},{z,-1,1},PlotPoints->5,Axes->True,ViewPoint->{30,10,5},AxesLabel->{x,y,z}];
Show[one,other]

Show[one,other]

Show[one,other,PlotRange->{{-1.1`,1.1`},{0.48`,0.52`},{-1.1`,1.1`}},AxesLabel->{"x",None,"z"},Ticks->{Automatic,None,Automatic}]

Show[one,other,PlotRange->{{-1.1`,1.1`},{0.78`,0.82`},{-1.1`,1.1`}},AxesLabel->{"x",None,"z"},Ticks->{Automatic,None,Automatic}]

Solve[{x^2+z^2==1,y^2+z^2==1},{x,y}]

PROBLEMS 9, 10:
  The following graphs might be useful.

Clear[F,x,y,z,one];
F[x_,y_,z_]=(Sqrt[1-(x^2)])-z;
Print["z=",(Sqrt[1-(x^2)])];
one=ContourPlot3D[F[x,y,z]==0,{x,-1,1},{y,0,1},{z,-1,1},PlotPoints->5,Axes->True,ViewPoint->{30,10,5},AxesLabel->{x,y,z}]

Clear[F,x,y,z,one];
F[x_,y_,z_]=-(Sqrt[1-(x^2)])-z;
Print["z=",-(Sqrt[1-(x^2)])];
one=ContourPlot3D[F[x,y,z]==0,{x,-1,1},{y,0,1},{z,-1,1},PlotPoints->5,Axes->True,ViewPoint->{30,10,5},AxesLabel->{x,y,z}]

Clear[F,x,y,z,one];
F[x_,y_,z_]=1-(x^2)-(z^2)-(y^2);
Print["y=",(Sqrt[1-(x^2)-(z^2)])];
one=ContourPlot3D[F[x,y,z]==0,{x,-1,1},{y,-1,1},{z,-1,1},PlotPoints->5,Axes->True,PlotRange->{{-1,1},{0,1},{-1,1}},ViewPoint->{30,10,5},AxesLabel->{x,y,z}]

Clear[F,x,y,z,two];
F[x_,y_,z_]=y;
Print["y=0"];
two=ContourPlot3D[F[x,y,z]==0,{x,-1,1},{y,-0.01`,1},{z,-1,1},PlotPoints->5,Axes->True,PlotRange->{{-1,1},{-1,1},{-1,1}},ViewPoint->{30,10,5},AxesLabel->{x,y,z}]

Show[one,two]

EVALUATING INTEGRALS:
  You can edit the following cell to evaluate a triple integral.

f[x_,y_,z_]=1.;

(∫_2^4) ((∫_(-Sqrt[16-z^2])^(Sqrt[16-z^2])) ((∫_(-Sqrt[16-z^2-x^2])^(Sqrt[16-z^2-x^2])) f[x,y,z] \[DifferentialD]y) \[DifferentialD]x) \[DifferentialD]z

+++++++++++++++++++++++++++++++++++++++++++++++++++

PROBLEM 26:

f[x_,y_]=6-2*x-3*y;
oneslice=ParametricPlot3D[{x,y,4},{y,0,2/3},{x,0,1-3/2*y},ViewPoint->{20,2,2}];
otherslice=ParametricPlot3D[{x,y,1},{y,0,5/3},{x,0,5/2-3/2*y},ViewPoint->{20,2,2}];
thegraph=Plot3D[f[x,y],{x,0,3},{y,0,2},PlotRange->{0,6},ViewPoint->{20,2,2},PlotStyle->Opacity[0.6]]
Show[thegraph,oneslice,otherslice]