2. (a) Write a parameterization r(u, v) for the surface that is the part of the plane z = 4+1-y that lies above the (x, y)-rectangle [0,3] x [0,1]. r(u,v) = Bounds for u and v: (b) Let S be the part of the plane z = 4+x-y that you just parameterized, oriented upward. Let F be the vector field F(x, y, z) = (3, 21, 5). Evaluate F. ds directly. Show all of your steps. (c) On the back, draw a picture that explains the meaning of S F.dS in the problem you just did here.
2. (a) Write a parameterization r(u, v) for the surface that is the part of the plane z = 4+1-y that lies above the (x, y)-rectangle [0,3] x [0,1]. r(u,v) = Bounds for u and v: (b) Let S be the part of the plane z = 4+x-y that you just parameterized, oriented upward. Let F be the vector field F(x, y, z) = (3, 21, 5). Evaluate F. ds directly. Show all of your steps. (c) On the back, draw a picture that explains the meaning of S F.dS in the problem you just did here.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please do NOT use Stokes' Theorem and make sure to include a picture or sketch explaining the meaning for part 2c.
![2. (a) Write a parameterization r(u, v) for the surface that is the part of the plane z = 4+1-y that lies
above the (x, y)-rectangle [0,3] x [0,1].
r(u,v) =
Bounds for u and v:
(b) Let S be the part of the plane z = 4+x-y that you just parameterized, oriented upward.
Let F be the vector field F(x, y, z) = (3, 21, 5).
Evaluate
F. ds directly. Show all of your steps.
(c) On the back, draw a picture that explains the meaning of
S
F.dS in the problem you just did here.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf909276-6ad3-4144-b98c-235c5a32e436%2F36ba3e57-4b18-469b-a0b6-339f115eb8c8%2Fy3eogr4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. (a) Write a parameterization r(u, v) for the surface that is the part of the plane z = 4+1-y that lies
above the (x, y)-rectangle [0,3] x [0,1].
r(u,v) =
Bounds for u and v:
(b) Let S be the part of the plane z = 4+x-y that you just parameterized, oriented upward.
Let F be the vector field F(x, y, z) = (3, 21, 5).
Evaluate
F. ds directly. Show all of your steps.
(c) On the back, draw a picture that explains the meaning of
S
F.dS in the problem you just did here.
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