Example 1

Plot3D[x^2+y^2+4x*y,{x,-2,2},{y,-2,2},AxesLabel->{x,y,z},ViewPoint->{1,1,1}]

Manipulate[Show[Plot3D[x^2+y^2+4x*y,{x,-2,2},{y,-2,2},AxesLabel->{x,y,z},ViewPoint->{1,1,1}],ContourPlot3D[y==Tan[T]*x,{x,-2,2},{y,-2,2},{z,-24,24}]],{T,0,2Pi}]

Examples 2a and 2b

Plot3D[x^4-y^4,{x,-2,2},{y,-2,2},AxesLabel->{x,y,z},ViewPoint->{1,1,1}]

Plot3D[x^4+y^4,{x,-2,2},{y,-2,2},AxesLabel->{x,y,z},ViewPoint->{1,1,1}]

Example 3 (14.7 #7)

Plot3D[x^4+y^4-4x*y+2,{x,-2,2},{y,-2,2},AxesLabel->{x,y,z},ViewPoint->{1,1,1}]

Manipulate[Show[Plot3D[x^4+y^4-4x*y+2,{x,-2,2},{y,-2,2},AxesLabel->{x,y,z},ViewPoint->{1,1,1}],ContourPlot3D[y==Tan[T]*x,{x,-2,2},{y,-2,2},{z,0,32}]],{T,0,2Pi}]

Example 4 (14.7 #31)

Plot3D[x^2+y^2+x^2*y+4,{x,-1,1},{y,-1,1},AxesLabel->{x,y,z},ViewPoint->{1,1,1},PlotRange->{4,8}]

Example 5 (14.7 #35)

Plot3D[2x^3+y^4,{x,-1,1},{y,-1,1},RegionFunction->Function[{x,y,z},x^2+y^2≤1],AxesLabel->{x,y,z},ViewPoint->{1,1,1}]