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Plot 3D Ln(x^2) Function?

Qian Lu

Posted 7 years ago

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!

POSTED BY: Qian Lu

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Mariusz Iwaniuk

Mariusz Iwaniuk, engineer, math hobbyist.

Posted 7 years ago

You made a syntax mistake.Try: RevolutionPlot3D[0.5Log[x^2], {x, 0, 1}, RevolutionAxis -> {0, 0, 1},PlotStyle -> FaceForm[Red, Blue]] Create a thick surface for 3D printing: RevolutionPlot3D[0.5Log[x^2], {x, 0.1, 1}, RevolutionAxis -> {0, 0, 1}, PlotTheme -> "ThickSurface", MaxRecursion -> 4] Regards,MI

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

POSTED BY: Mariusz Iwaniuk

Qian Lu

Posted 7 years ago

Thank you very much! But I am still confused about 2 questions: (1) We can only use Log function instead of Ln function? (2) How do I set the limit of the height? Because I only want this function's height goes from (y=-0.6 to y=0) I really appreciate your time!

POSTED BY: Qian Lu

Mariusz Iwaniuk

Mariusz Iwaniuk, engineer, math hobbyist.

Posted 7 years ago

Log[x] 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[0.5Ln[x^2], {x, 0, 1}, RevolutionAxis -> {0, 0, 1}, PlotStyle -> FaceForm[Red, Blue], PlotRange -> {Automatic, {-0.6, 0}, Automatic}] RevolutionPlot3D[0.5Ln[x^2], {x, 0, 1}, RevolutionAxis -> {0, 0, 1}, PlotStyle -> FaceForm[Red, Blue], PlotRange -> {{-0.6, 0}, {-0.6, 0}, Automatic}]

Log[x] 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}]

POSTED BY: Mariusz Iwaniuk

Qian Lu

Posted 7 years ago

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?

POSTED BY: Qian Lu

Mariusz Iwaniuk

Mariusz Iwaniuk, engineer, math hobbyist.

Posted 7 years ago

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]

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]

enter image description here

 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]

enter image description here