(3) Consider the surface of revolution H = {(x, y, z) € R³ | x² + z² = (² + cos³½)²)}. (a) Find the tangent plane to H at (2/2)) 3 π, 2√2 (See also (Q7) of Problem Sheet 7.) (b) Find the unit normals to H at (23/2,π, 2√2 3 2√2 (c) Which of the two unit normals in (b) represents the "outward-facing" side of H? (For part (c), you do not have to prove the answer. You can find the answer by sketching H and the appropriate normals and then inspecting your sketch.)
(3) Consider the surface of revolution H = {(x, y, z) € R³ | x² + z² = (² + cos³½)²)}. (a) Find the tangent plane to H at (2/2)) 3 π, 2√2 (See also (Q7) of Problem Sheet 7.) (b) Find the unit normals to H at (23/2,π, 2√2 3 2√2 (c) Which of the two unit normals in (b) represents the "outward-facing" side of H? (For part (c), you do not have to prove the answer. You can find the answer by sketching H and the appropriate normals and then inspecting your sketch.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
Related questions
Question
![(3)
Consider the surface of revolution
H = {(x, y, z) € R³ | x² + z² = (² + cos³½)²)}.
(a) Find the tangent plane to H at (2/2))
3
π,
2√2
(See also (Q7) of Problem Sheet 7.)
(b) Find the unit normals to H at (23/2,π,
2√2
3
2√2
(c) Which of the two unit normals in (b) represents the "outward-facing" side of H?
(For part (c), you do not have to prove the answer. You can find the answer by sketching H
and the appropriate normals and then inspecting your sketch.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Face6f3b2-9ef6-4761-9333-1358c52634df%2F5c4296fc-9759-4a5b-ac99-00f0b9736f29%2Fi9xuycc_processed.png&w=3840&q=75)
Transcribed Image Text:(3)
Consider the surface of revolution
H = {(x, y, z) € R³ | x² + z² = (² + cos³½)²)}.
(a) Find the tangent plane to H at (2/2))
3
π,
2√2
(See also (Q7) of Problem Sheet 7.)
(b) Find the unit normals to H at (23/2,π,
2√2
3
2√2
(c) Which of the two unit normals in (b) represents the "outward-facing" side of H?
(For part (c), you do not have to prove the answer. You can find the answer by sketching H
and the appropriate normals and then inspecting your sketch.)
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