# Plot 3D Ln(x^2) Function?

Posted 8 months ago
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 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!
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Posted 8 months ago
 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 8 months 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 8 months 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[0.5*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 8 months 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?
 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]