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We cannot plot the 4D graph (x, y, z, w) of a function of three variables w = f(x, y, z), but we can look at its 3D level surfaces f(x, y, z) = c. Given the function of three variables w = x + 2², choose five distinct constants C₁, C2, C3, C4, and c5 to plot five level surfaces x + z² = c; in one figure using Contour Plot3D. To create a nice picture, pick the appropriate range for each variable and play with the option Contour Style → Opacity to make all the surfaces clearly seen in the combined plot.

We cannot plot the 4D graph (x, y, z, w) of a function of three variables w = f(x, y, z), but we can look at its 3D level surfaces f(x, y, z) = c. Given the function of three variables w = x + 2², choose five distinct constants C₁, C2, C3, C4, and c5 to plot five level surfaces x + z² = c; in one figure using Contour Plot3D. To create a nice picture, pick the appropriate range for each variable and play with the option Contour Style → Opacity to make all the surfaces clearly seen in the combined plot.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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We cannot plot the 4D graph \((x, y, z, w)\) of a function of three variables \(w = f(x, y, z)\), but we can look at its 3D level surfaces \(f(x, y, z) = c\). Given the function of three variables \(w = x + z^2\), choose five distinct constants \(c_1, c_2, c_3, c_4, \text{ and } c_5\) to plot five level surfaces \(x + z^2 = c_i\) in one figure using \textit{ContourPlot3D}. To create a nice picture, pick the appropriate range for each variable and play with the option \text{ContourStyle} \(\rightarrow\) \text{Opacity} to make all the surfaces clearly seen in the combined plot.
Transcribed Image Text:We cannot plot the 4D graph \((x, y, z, w)\) of a function of three variables \(w = f(x, y, z)\), but we can look at its 3D level surfaces \(f(x, y, z) = c\). Given the function of three variables \(w = x + z^2\), choose five distinct constants \(c_1, c_2, c_3, c_4, \text{ and } c_5\) to plot five level surfaces \(x + z^2 = c_i\) in one figure using \textit{ContourPlot3D}. To create a nice picture, pick the appropriate range for each variable and play with the option \text{ContourStyle} \(\rightarrow\) \text{Opacity} to make all the surfaces clearly seen in the combined plot.
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