fplot=Plot3D[{16-x^2-y^2},{x,-5,5},{y,-5,5},PlotRange->{0,20}];
line=ParametricPlot3D[{2+t,0,12-4t},{t,-15,15},PlotStyle->{Thickness[.02],Black}];
line2=ParametricPlot3D[{2+t,2,8-4t},{t,-15,15},PlotStyle->{Thickness[.02],Blue}];
Show[fplot,line,line2]

f[x_,y_]:=25-x^2-y^2
ContourPlot[{ f[x,y]==24,f[x,y] ==20, f[x,y]==15, f[x,y]==10, f[x,y]==5},{x,-5,5},{y,-5,5},PlotLegends->"Expressions",LabelStyle->Directive[FontSize->20]]

g[x_,y_]:=Sqrt[x^2+y^2]
ContourPlot[{g[x,y]==1,g[x,y]==2,g[x,y]==3,g[x,y]==4,g[x,y]==5},{x,-5,5},{y,-5,5},PlotLegends->"Expressions",LabelStyle->Directive[FontSize->20]]

ContourPlot[{x^2-y^2==-4,x^2-y^2==-1,x^2-y^2==0,x^2-y^2==1,x^2-y^2==4},{x,-3,3},{y,-3,3},PlotLegends->"Expressions",LabelStyle->Directive[FontSize->20]]

(Legended[, (LineLegend[(x^2)-(y^2)==-4, (x^2)-(y^2)==-1, (x^2)-(y^2)==0, (x^2)-(y^2)==1, (x^2)-(y^2)==4])])

Plot3D[{-(x^2+4y^2),-8-4(x-2)-8(y-1)},{x,1,3},{y,0,2}]

Plot3D[{y E^(x/y), E + E(x-1)}, {x,0,2},{y,0,2}]

E^(1.1)

1.1E

plot=ContourPlot[{x*y-Sin[x]==-9,x*y-Sin[x]==-Pi,x*y-Sin[x]==-1,x*y-Sin[x]==0,x*y-Sin[x]==1,x*y-Sin[x]==Pi,x*y-Sin[x]==9},{x,-5,5},{y,-5,5},PlotLegends->"Expressions",LabelStyle->Directive[FontSize->20]]

vect=Graphics[Arrow[{{Pi,1},{2+Pi,1+Pi}}]];
vect3d=Graphics3D[{Thickness[.03],Arrow[{{Pi,1,Pi},{2+Pi,1+Pi,Pi+Sqrt[4+Pi^2]}}]}]
point3d=Graphics3D[{AbsolutePointSize[20],Point[{Pi,1,Pi}]}]

Show[vect,plot]

plot3d=Plot3D[x*y-Sin[x],{x,-5,5},{y,-5,5}]

Show[plot3d,vect3d,point3d]

g[x_,y_,z_]:=x y + z;
surfacecontour=ContourPlot3D[{g[x,y,z]==-4,g[x,y,z]==-1,g[x,y,z]==0,g[x,y,z]==1},{x,-3,3},{y,-3,3},{z,-3,3},PlotLegends->"Expressions"]

surfacegradient=Graphics3D[{Thickness[.01],Arrow[{{-1,0,1},{-1,-1,2}}]}];
surfacepoint3d=Graphics3D[{AbsolutePointSize[10],Point[{-1,0,1}]}];
Show[surfacecontour,surfacegradient,surfacepoint3d]

Plot[{x^2,x^2+1,x^2+4,x^2+9},{x,-2,2}]

Plot[{x^2,x^2+1,x^2+4,x^2+9,2x-1,2x,2x+3,2x+8},{x,-2,2},PlotStyle->{Black,Black,Black,Black,Blue,Blue,Blue,Blue}]

f[x_,y_]:=Cos[3x+2y]+2Sin[x-y]
ftaylor[x_,y_]:=1+2x-2y-9x^2/2-6x y -2y^2

Plot3D[{f[x,y],ftaylor[x,y]},{x,-2,2},{y,-2,2},PlotRange->{-3,3}]

ContourPlot[{f[x,y]==-1,f[x,y]==-2,f[x,y]==0,f[x,y]==2,f[x,y]==1},{x,-1,1},{y,-1,1},PlotLegends->"Expressions"]

ContourPlot[{1+2x-2y==-1,1+2x-2y==-2,1+2x-2y==0,1+2x-2y==2,1+2x-2y==1},{x,-1,1},{y,-1,1},PlotLegends->"Expressions"]

ContourPlot[{ftaylor[x,y]==-1,ftaylor[x,y]==-2,ftaylor[x,y]==0,ftaylor[x,y]==2,ftaylor[x,y]==1},{x,-1,1},{y,-1,1},PlotLegends->"Expressions"]

Plot3D[{E^(x y),1 + 2x^2 + x y/2},{x,-1,1},{y,1,3}]

ContourPlot[{E^(x y) ==1/2,E^(x y) ==1,E^(x y) ==2,E^(x y) ==3},{x,-1,1},{y,1,3},PlotLegends->"Expressions"]

ContourPlot[{1+2x==1/2,1+2x ==1,1+2x==2,1+2x ==3},{x,-1,1},{y,1,3},PlotLegends->"Expressions"]

ContourPlot[{1+2x^2 + x y==1/2,1+2x^2 + x y ==1,1+2x^2 + x y==2,1+2x^2 + x y==3},{x,-1,1},{y,1,3},PlotLegends->"Expressions"]

ContourPlot[{1/(x y) == 1/8,1/(x y) == 1/4,1/(x y) == 1/2,1/(x y) == 1,1/(x y) == 2,1/(x y) == 3},{x,0,2},{y,1,3},PlotLegends->"Expressions"]

Q[x_,y_]:=1/2 - (x-1)/2 - (y-2)/2+(x-1)^2/2 + (x-1)(y-2)/4 + (y-2)^2/8

ContourPlot[{Q[x,y] == 1/8,Q[x,y] == 1/4,Q[x,y] == 1/2,Q[x,y]== 1,Q[x,y] == 2,Q[x,y] == 3},{x,0,2},{y,1,3},PlotLegends->"Expressions"]