Practice Problems 13.1 and 13.8
> with(plots):
13.1 number 11
> contourplot(y-x^2, x=-3..3, y=-3..3, contours=[-3, -2, -1, 0, 1, 2, 3], coloring=[orange, blue]);
> contourplot(x-y^2, x=-3..3, y=-3..3, contours=[-3, -2, -1, 0, 1, 2, 3], coloring=[orange, blue]);
> plot3d(y-x^2, x=-3..3, y=-3..3);
> plot3d(x-y^2, x=-3..3, y=-3..3);
13.1 number 13
> contourplot(ln(4*x^2+y^2), x=-3..3, y=-3..3);
13.1 number 21
> plot3d(sqrt(x^2+y^2), x=-5..5, y=-5..5);
> a:=contourplot(sqrt(x^2+y^2), x=-5..5, y=-5..5, contours=[0, 1, 2, 3, 4, 5], coloring=[orange, blue]):
> b:=pointplot([3,4], symbol=circle, symbolsize=20):
> display(a,b);
Limit Practice II. 1
> plot3d(x*y/(x^2+y^2), x=-0.1..0.1, y=-0.1..0.1);
> f := (x,y) -> (x*y)/(x^2+y^2);
> g1 := y=x;
> g2 := y=0;
> with(plots):
> with(plottools):
> FP := plot3d(f(x,y), x=-0.1..0.1, y=-0.1..0.1):
> GP1 := implicitplot(g1, x=-0.1..0.1, y=-0.1..0.1, thickness=2, color=black):
> GP2 := implicitplot(g2, x=-0.1..0.1, y=-0.1..0.1, thickness=2, color=black):
> T := transform((x,y)->[x,y,f(x,y)]):
> display([FP,T(GP1), T(GP2)]);
Limit Practice II. 2
> plot3d(x^3+y/(x^2+y^2), x=-0.1..0.1, y=-0.1..0.1, view=-1..1);
> f := (x,y) -> (x^3+y)/(x^2+y^2);
> g1 := y=x;
> g2 := y=0;
> with(plots):
> with(plottools):
> FP := plot3d(f(x,y), x=-0.1..0.1, y=-0.1..0.1):
> FQ: plot3d(f(x,y), x=-0.1..0.1, y=-0.1..0.1, view=0..100):
> GP1 := implicitplot(g1, x=-0.1..0.1, y=-0.1..0.1, thickness=3, color=red):
> GP2 := implicitplot(g2, x=-0.1..0.1, y=-0.1..0.1, thickness=3, color=blue):
> T := transform((x,y)->[x,y,f(x,y)]):
> display([FP,T(GP1), T(GP2)]);
> FP := plot3d(f(x,y), x=-0.1..0.1, y=-0.1..0.1, view=-1..100):
> GP1 := implicitplot(g1, x=-0.1..0.1, y=-0.1..0.1, thickness=3, color=red):
> GP2 := implicitplot(g2, x=-0.1..0.1, y=-0.1..0.1, thickness=3, color=blue):
> T := transform((x,y)->[x,y,f(x,y)]):
> display([FP,T(GP1), T(GP2)]);
Limit Practice II. 3
> plot3d(x^3+2*y^5/(x^2+y^2), x=-0.1..0.1, y=-0.1..0.1);
Limit Practice II. 4
> plot3d(x^2*y+x*y^2/(x^2+y^2), x=-0.1..0.1, y=-0.1..0.1);
Limit Practice III. 1
> f := (x,y) -> (3*x^3+2*y^2)/(x^2+y^2);
> g1 := x=0;
> g2 := y=0;
> with(plots):
> with(plottools):
> FP := plot3d(f(x,y), x=-0.1..0.1, y=-0.1..0.1):
> FQ: plot3d(f(x,y), x=-0.1..0.1, y=-0.1..0.1, view=0..100):
> GP1 := implicitplot(g1, x=-0.1..0.1, y=-0.1..0.1, thickness=4, color=red):
> GP2 := implicitplot(g2, x=-0.1..0.1, y=-0.1..0.1, thickness=4, color=blue):
> T := transform((x,y)->[x,y,f(x,y)]):
> display([FP,T(GP1), T(GP2)]);
Limit Practice II. 2
> f := (x,y) -> (5*x*y)/(x^2+y^2);
> g1 := y=x;
> g2 := y=0;
> with(plots):
> with(plottools):
> FP := plot3d(f(x,y), x=-0.1..0.1, y=-0.1..0.1):
> FQ: plot3d(f(x,y), x=-0.1..0.1, y=-0.1..0.1, view=0..100):
> GP1 := implicitplot(g1, x=-0.1..0.1, y=-0.1..0.1, thickness=4, color=red):
> GP2 := implicitplot(g2, x=-0.1..0.1, y=-0.1..0.1, thickness=4, color=blue):
> T := transform((x,y)->[x,y,f(x,y)]):
> display([FP,T(GP1), T(GP2)]);