5. Consider the surface described by the parameterization r(u, v): = ((2 + sin v) cos u, (2 + sin v) sin u, u + cos v) for - < u <∞ and 0 ≤ v ≤ 2π. Find all points on the surface where the tangent plane is parallel to the xz-plane. Hint: see the book for a picture of this surface.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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5. Consider the surface described by the parameterization
r(u, v) = ((2 + sin v) cos u, (2 + sin v) sin u, u + cos v)
for - < u < ∞ and 0 ≤ v ≤ 2π. Find all points on the surface where the tangent plane is
parallel to the xz-plane. Hint: see the book for a picture of this surface.
Transcribed Image Text:5. Consider the surface described by the parameterization r(u, v) = ((2 + sin v) cos u, (2 + sin v) sin u, u + cos v) for - < u < ∞ and 0 ≤ v ≤ 2π. Find all points on the surface where the tangent plane is parallel to the xz-plane. Hint: see the book for a picture of this surface.
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