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3. (a) Verify that the function X(u, v) = ((u + v), (u − v), 4uv) satisfies the equation of a - hyperbolic paraboloid, x² - y² = z. (b) To see if X(u, v) from above forms a regular patch, we need to have X₁ × X₁, ‡ 0. Check to see if there are any u and v for which this cross product equals 0.

3. (a) Verify that the function X(u, v) = ((u + v), (u − v), 4uv) satisfies the equation of a - hyperbolic paraboloid, x² - y² = z. (b) To see if X(u, v) from above forms a regular patch, we need to have X₁ × X₁, ‡ 0. Check to see if there are any u and v for which this cross product equals 0.

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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3. (a) Verify that the function X(u, v) = ((u + v), (u – v), 4uv) satisfies the equation of a hyperbolic paraboloid, x²-y²=Z. (b) To see if X(u, v) from above forms a regular patch, we need to have X₁ × X₁ #0. Check to see if there are any u and v for which this cross product equals 0.
Transcribed Image Text:3. (a) Verify that the function X(u, v) = ((u + v), (u – v), 4uv) satisfies the equation of a hyperbolic paraboloid, x²-y²=Z. (b) To see if X(u, v) from above forms a regular patch, we need to have X₁ × X₁ #0. Check to see if there are any u and v for which this cross product equals 0.
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