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We cannot generally graph functions of three variables, such as f(x, y, z) = x² + y² – 2². We can, nevertheless, graph its level surfaces. Graph the level surfaces of f (x, y, z) given by f(x,y, z) = 0, f(x, y, z) = 1, and f(x, y, z) = 9. (Hint: what quadric surfaces to these describe? Considering the level curve z = 0 on the surfaces f(x,y, z) = 1 and f(x, y, z) = 9 will give a helpful sense of scale.)

We cannot generally graph functions of three variables, such as f(x, y, z) = x² + y² – 2². We can, nevertheless, graph its level surfaces. Graph the level surfaces of f (x, y, z) given by f(x,y, z) = 0, f(x, y, z) = 1, and f(x, y, z) = 9. (Hint: what quadric surfaces to these describe? Considering the level curve z = 0 on the surfaces f(x,y, z) = 1 and f(x, y, z) = 9 will give a helpful sense of scale.)

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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O We cannot generally graph functions of three variables, such as f(r, y, z) = x² + y² – z². We can, nevertheless, graph its level surfaces. Graph the level surfaces of f(x, y, z) given by f(x, y, z) = 0, f(x,y,z) = 1, and f(x,y, z) = 9. (Hint: what quadric surfaces to these describe? Considering the level curve z = 0 on the surfaces f(x,y, z) = 1 and f(x, y, z) = 9 will give a helpful sense of scale.)
Transcribed Image Text:O We cannot generally graph functions of three variables, such as f(r, y, z) = x² + y² – z². We can, nevertheless, graph its level surfaces. Graph the level surfaces of f(x, y, z) given by f(x, y, z) = 0, f(x,y,z) = 1, and f(x,y, z) = 9. (Hint: what quadric surfaces to these describe? Considering the level curve z = 0 on the surfaces f(x,y, z) = 1 and f(x, y, z) = 9 will give a helpful sense of scale.)
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