Tangent Lines to Intersecting Surfaces In Exercises 15-20, find parametric equations for the line tangent to the curve of intersection of the surfaces at the given point. 15. Surfaces: x + y² + 2z = 4, x = 1 Point: (1, 1, 1) 16. Surfaces: xyz = 17 Surfaces: 1, x² + 2y² + 3z² = 6 Point: (1, 1, 1) 1-2 + 2y + 27 = 4 y = 1
Tangent Lines to Intersecting Surfaces In Exercises 15-20, find parametric equations for the line tangent to the curve of intersection of the surfaces at the given point. 15. Surfaces: x + y² + 2z = 4, x = 1 Point: (1, 1, 1) 16. Surfaces: xyz = 17 Surfaces: 1, x² + 2y² + 3z² = 6 Point: (1, 1, 1) 1-2 + 2y + 27 = 4 y = 1
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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Transcribed Image Text:Tangent Lines to Intersecting Surfaces
In Exercises 15-20, find parametric equations for the line tangent to
the curve of intersection of the surfaces at the given point.
15. Surfaces: x + y² + 2z = 4, x = 1
Point: (1, 1, 1)
16. Surfaces: xyz = 1, x² + 2y² + 3z² = 6
Point: (1, 1, 1)
17. Surfaces: x² + 2y + 2z = 4, y = 1
Point: (1, 1, 1/2)
18. Surfaces: x + y² + z = 2, y = 1
Point: (1/2, 1, 1/2)
19. Surfaces: x³ + 3x²y² + y² + 4xy z² = 0, dy) nearby,
x² + y² + z²
= 11
—
Point:
(1, 1, 3)
20. Surfaces: x² + y² = 4, x² + y² - z = 0
Point: (√2, √2, 4)
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