Here's a picture of the parametric surface r(u, v) = (u cos v, u sin v, uv) for 0 ≤ u ≤ 12,0 ≤ v ≤ 4π, together with a sketch of the parameter domain: 4m 15/4 7π/2 13π/4 3T 11π/4 5π/2 9π/4 2π 7π/4 3π/2 5π/4 ㅠ 3п/4 π/2 π/4 10 12 Y The blue piece in the surface corresponds to the blue piece in the parameter domain. Which of the following is the best estimate for the area of the blue piece of the surface? Explain your reasoning. 1.5 10 40 70 Hint: You don't need to do any integrating here; instead, think about how we came up with the surface area formula for dS. To save you some computation, here's Tux Tv: Tux T = (usin v-uv cos v, -uv sin v - u cos v, u).
Here's a picture of the parametric surface r(u, v) = (u cos v, u sin v, uv) for 0 ≤ u ≤ 12,0 ≤ v ≤ 4π, together with a sketch of the parameter domain: 4m 15/4 7π/2 13π/4 3T 11π/4 5π/2 9π/4 2π 7π/4 3π/2 5π/4 ㅠ 3п/4 π/2 π/4 10 12 Y The blue piece in the surface corresponds to the blue piece in the parameter domain. Which of the following is the best estimate for the area of the blue piece of the surface? Explain your reasoning. 1.5 10 40 70 Hint: You don't need to do any integrating here; instead, think about how we came up with the surface area formula for dS. To save you some computation, here's Tux Tv: Tux T = (usin v-uv cos v, -uv sin v - u cos v, u).
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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Question
10
Transcribed Image Text:Here's a picture of the parametric surface r(u, v) = (u cos v, u sin v, uv) for 0 ≤ u ≤ 12,0 ≤ v ≤ 4π,
together with a sketch of the parameter domain:
4m
15/4
7π/2
13π/4
3T
11π/4
5π/2
9π/4
2π
7π/4
3π/2
5π/4
ㅠ
3п/4
π/2
π/4
10 12
Y
The blue piece in the surface corresponds to the blue piece in the parameter domain. Which of the
following is the best estimate for the area of the blue piece of the surface? Explain your reasoning.
1.5 10 40
70
Hint: You don't need to do any integrating here; instead, think about how we came up with the surface
area formula for dS. To save you some computation, here's Tux Tv:
Tux T = (usin v-uv cos v, -uv sin v - u cos v, u).
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