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Decide whether the level surfaces of each function are concentric circular cylinders, concentric spheres, cones, elliptical paraboloids, hyperbolic paraboloids, hyperboloids of one sheet, hyperboloids of two sheets, parabolic cylinders, or parallel planes. ? ? ? ? ? ? ? ? 1. f(x, y, z) = 4x² + y² - Z 2. f(x, y, z) = sin(√√6(x² + y² + z²)) 3. f(x, y, z) = cos(6x + y + z) 4. f(x, y, z) = x + y = 2z 5. f(x, y, z) = ln(√√/y² + z²) 46. f(x, y, z) = e¯(x²+y²+z²) 7. f(x, y, z) = 3x² - y 8. f(x, y, z) = 9y² - 3x² - z

Decide whether the level surfaces of each function are concentric circular cylinders, concentric spheres, cones, elliptical paraboloids, hyperbolic paraboloids, hyperboloids of one sheet, hyperboloids of two sheets, parabolic cylinders, or parallel planes. ? ? ? ? ? ? ? ? 1. f(x, y, z) = 4x² + y² - Z 2. f(x, y, z) = sin(√√6(x² + y² + z²)) 3. f(x, y, z) = cos(6x + y + z) 4. f(x, y, z) = x + y = 2z 5. f(x, y, z) = ln(√√/y² + z²) 46. f(x, y, z) = e¯(x²+y²+z²) 7. f(x, y, z) = 3x² - y 8. f(x, y, z) = 9y² - 3x² - z

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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### Problem Statement Decide whether the level surfaces of each function are: - Concentric circular cylinders - Concentric spheres - Cones - Elliptical paraboloids - Hyperbolic paraboloids - Hyperboloids of one sheet - Hyperboloids of two sheets - Parabolic cylinders - Parallel planes ### Functions to Analyze 1. \( f(x, y, z) = 4x^2 + y^2 - z \) 2. \( f(x, y, z) = \sin\left(\sqrt{6(x^2 + y^2 + z^2)}\right) \) 3. \( f(x, y, z) = \cos(6x + y + z) \) 4. \( f(x, y, z) = x + y - 2z \) 5. \( f(x, y, z) = \ln(\sqrt{y^2 + z^2}) \) 6. \( f(x, y, z) = e^{-(x^2 + y^2 + z^2)} \) 7. \( f(x, y, z) = 3x^2 - y \) 8. \( f(x, y, z) = 9y^2 - 3x^2 - z \) ### Instructions Evaluate each function to determine the geometric form of its level surfaces based on the provided categories.
Transcribed Image Text:### Problem Statement Decide whether the level surfaces of each function are: - Concentric circular cylinders - Concentric spheres - Cones - Elliptical paraboloids - Hyperbolic paraboloids - Hyperboloids of one sheet - Hyperboloids of two sheets - Parabolic cylinders - Parallel planes ### Functions to Analyze 1. \( f(x, y, z) = 4x^2 + y^2 - z \) 2. \( f(x, y, z) = \sin\left(\sqrt{6(x^2 + y^2 + z^2)}\right) \) 3. \( f(x, y, z) = \cos(6x + y + z) \) 4. \( f(x, y, z) = x + y - 2z \) 5. \( f(x, y, z) = \ln(\sqrt{y^2 + z^2}) \) 6. \( f(x, y, z) = e^{-(x^2 + y^2 + z^2)} \) 7. \( f(x, y, z) = 3x^2 - y \) 8. \( f(x, y, z) = 9y^2 - 3x^2 - z \) ### Instructions Evaluate each function to determine the geometric form of its level surfaces based on the provided categories.
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