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Let f(r, y, z) = r² – 21 + y² – z. (a) Show that the equation of the level surface that passes through the point (1,0,3) is z = r² – 2r + y² + 4 . (b) Find the domain and range of z. (c) Sketch the level curves at z = 3, 4, 5. (d) Hence sketch the level surface.

Let f(r, y, z) = r² – 21 + y² – z. (a) Show that the equation of the level surface that passes through the point (1,0,3) is z = r² – 2r + y² + 4 . (b) Find the domain and range of z. (c) Sketch the level curves at z = 3, 4, 5. (d) Hence sketch the level surface.

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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1. Let f(r, y, 2) =r² – 2r + y? – 2. (a) Show that the equation of the level surface that passes through the point (1,0, 3) is z = 1² – 2r + y² + 4. (b) Find the domain and range of z. (c) Sketch the level curves at z = 3, 4, 5. (d) Hence sketch the level surface.
Transcribed Image Text:1. Let f(r, y, 2) =r² – 2r + y? – 2. (a) Show that the equation of the level surface that passes through the point (1,0, 3) is z = 1² – 2r + y² + 4. (b) Find the domain and range of z. (c) Sketch the level curves at z = 3, 4, 5. (d) Hence sketch the level surface.
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