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7. xy = 1

7. xy = 1

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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David Frazier / Spirit / Corbis A satellite dish reflects signals to the focus of a paraboloid. Mark C. Burnett / Science Source Nuclear reactors have cooling towers in the shape of hyperboloids. 12.6 EXERCISES 1. (a) What does the equation y = x² represent as a curve in R2? (b) What does it represent as a surface in R³? (c) What does the equation z = y² represent? 3-8 Describe and sketch the surface. 3. x² + z² = 1 2. (a) Sketch the graph of y = e* as a curve in R². (b) Sketch the graph of y = e* as a surface in R³. (c) Describe and sketch the surface z = e. 4. 4x² + y² = 4 SA-REM 0910 642.EA 5. z = 1 − y² 7. xy = 1 Hyperboloids produce gear transmission. 6. y = z² 8. z = sin y 9. (a) Find and identify the traces of the quadric surface x² + y² = z² = 1 and explain why the graph looks like the graph of the hyperboloid of one sheet in Table 1. (b) If we change the equation in part (a) to x² - y² + z² = 1, how is the graph affected? (c) What if we change the equation in part (a) to - x² + y² + 2y = z² = 0?
Transcribed Image Text:David Frazier / Spirit / Corbis A satellite dish reflects signals to the focus of a paraboloid. Mark C. Burnett / Science Source Nuclear reactors have cooling towers in the shape of hyperboloids. 12.6 EXERCISES 1. (a) What does the equation y = x² represent as a curve in R2? (b) What does it represent as a surface in R³? (c) What does the equation z = y² represent? 3-8 Describe and sketch the surface. 3. x² + z² = 1 2. (a) Sketch the graph of y = e* as a curve in R². (b) Sketch the graph of y = e* as a surface in R³. (c) Describe and sketch the surface z = e. 4. 4x² + y² = 4 SA-REM 0910 642.EA 5. z = 1 − y² 7. xy = 1 Hyperboloids produce gear transmission. 6. y = z² 8. z = sin y 9. (a) Find and identify the traces of the quadric surface x² + y² = z² = 1 and explain why the graph looks like the graph of the hyperboloid of one sheet in Table 1. (b) If we change the equation in part (a) to x² - y² + z² = 1, how is the graph affected? (c) What if we change the equation in part (a) to - x² + y² + 2y = z² = 0?
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