I am doing a project for my college calculus class.
Revolve the region bonded by the graphs of y=0.5Ln(x^2), y=0, y=-0.6, x=0 about then y-axis
When I try to use Mathematica to graph the 3d mode, all I get is just a blank cube.
Please help me!!! Thank you!
You made a syntax mistake.Try:
RevolutionPlot3D[0.5*Log[x^2], {x, 0, 1}, RevolutionAxis -> {0, 0, 1},PlotStyle -> FaceForm[Red, Blue]]
Create a thick surface for 3D printing:
RevolutionPlot3D[0.5*Log[x^2], {x, 0.1, 1}, RevolutionAxis -> {0, 0, 1}, PlotTheme -> "ThickSurface", MaxRecursion -> 4]
Regards,MI
[Log[x]]1 gives the natural logarithm of x and function is builid-in,but we can defining:
Ln[x_] := Log[x];
Limit of the height we can adjust by PlotRange.
PlotRange → {{Range for X}, {Range for Y}, {Range for Z}}
Ln[x_] := Log[x];
RevolutionPlot3D[0.5*Ln[x^2], {x, 0, 1}, RevolutionAxis -> {0, 0, 1},
PlotStyle -> FaceForm[Red, Blue],
PlotRange -> {Automatic, {-0.6, 0}, Automatic}]
RevolutionPlot3D[0.5*Ln[x^2], {x, 0, 1}, RevolutionAxis -> {0, 0, 1},
PlotStyle -> FaceForm[Red, Blue],
PlotRange -> {{-0.6, 0}, {-0.6, 0}, Automatic}]
Thank you very much!!! You just saved my life!
May I ask you the last question?
This is a project of Math class to use functions to create a cup. I designed this cup with 7 functions. However, the middle part is just made of the function I asked you before and shifts down some units.
So I have trouble with combine all the 7 pieces of functions together. Could you please help me with that?
A simple way is to write in Piecewise than combine in Show.
ClearAll["Global`*"]; Remove["Global`*"]
f[x_] := Piecewise[{{Sqrt[-x + 1], 0 <= x <= 1}, {-1 + x,
1 <= x <= 3/2}, {2 - x, 3/2 <= x <= 2}, {-1 + x/2,
2 <= x <= 5/2}, {3/2 - x/2, 5/2 <= x <= 3}, {Sqrt[x - 3],
3 <= x <= 7/2}, {1/Sqrt[2], 7/2 <= x <= 5}}];
f2[x_] :=
Piecewise[{{Sqrt[-x + 1.05], 0 <= x <= 1}, {(x - 1)^2 + 0.05,
1 <= x <= 3/2}, {(x - 2)^2 + 0.05,
3/2 <= x <= 2}, {(x - 2)^2 + 0.05,
2 <= x <= 5/2}, {(x - 3)^2 + 0.05,
5/2 <= x <= 3}, {Sqrt[x - 3] + 0.05,
3 <= x <= 7/2}, {1/Sqrt[2] + 0.05, 7/2 <= x <= 5}}];
f3[x_] :=
Piecewise[{{Sqrt[-x + 1.05], 0 <= x <= 1}, {(x - 1)^3 + 0.05,
1 <= x <= 3/2}, {(x - 3/2)^3 + 0.05,
3/2 <= x <= 2}, {(x - 2)^2 + 0.05,
2 <= x <= 5/2}, {(x - 3)^2 + 0.05,
5/2 <= x <= 3}, {Sqrt[x - 3] + 0.05,
3 <= x <= 7/2}, {1/Sqrt[2] + 0.05, 7/2 <= x <= 5}}];
f4[x_] :=
Piecewise[{{Sqrt[-x + 1.05], 0 <= x <= 1}, {(x - 1) + 0.05,
1 <= x <= 3/2}, {-(x - 2) + 0.05,
3/2 <= x <= 2}, {(x - 2)^2 + 0.05,
2 <= x <= 5/2}, {(x - 3)^2 + 0.05,
5/2 <= x <= 3}, {Sqrt[x - 3] + 0.05,
3 <= x <= 7/2}, {1/Sqrt[2] + 0.05, 7/2 <= x <= 5}}];
Ln[x_] := Log[x];
f5[x_] :=
Piecewise[{{-Surd[x - 1, 3], 0 <= x <= 1}, {Exp[(x - 1)^2] - 0.95,
1 <= x <= 3/2}, {Exp[-(x - 1/2)^2] - 0.05,
3/2 <= x <= 2}, {(x - 2)^2 + 0.05,
2 <= x <= 5/2}, {(x - 3)^2 + 0.05,
5/2 <= x <= 3}, {Exp[(x - 3)^2] - 0.95,
3 <= x <= 3 + Sqrt[Ln[39/20]]}, {1,
3 + Sqrt[Ln[39/20]] <= x <= 6}}];
Plot[f4[x], {x, 0, 5}, PlotRange -> {Automatic, {0, 3/2}}, Exclusions -> None]
RevolutionPlot3D[f[x], {x, 0, 5}, RevolutionAxis -> {1, 0, 0},
Mesh -> None, Axes -> False, Boxed -> False, Exclusions -> None,
MaxRecursion -> 5]
RevolutionPlot3D[f2[x], {x, 0, 5}, RevolutionAxis -> {1, 0, 0},
Mesh -> None, Axes -> False, Boxed -> False, Exclusions -> None,
MaxRecursion -> 5]
RevolutionPlot3D[f3[x], {x, 0, 5}, RevolutionAxis -> {1, 0, 0},
Mesh -> None, Axes -> False, Boxed -> False, Exclusions -> None,
MaxRecursion -> 5]
RevolutionPlot3D[f4[x], {x, 0, 5}, RevolutionAxis -> {1, 0, 0},
Mesh -> None, Axes -> False, Boxed -> False, Exclusions -> None,
MaxRecursion -> 5]
RevolutionPlot3D[f5[x], {x, 0, 6}, RevolutionAxis -> {1, 0, 0},
Mesh -> None, Axes -> False, Boxed -> False, Exclusions -> None,
MaxRecursion -> 5]
Thank you very very very very very much!