C₁: closed circle, x² + y² = 9 C₂: closed circle, (x - 2)² + y² = 1 C3: closed circle, x² + y² = 4 C4: boundary of the closed box, -1 ≤ x ≤ 3, -1 ≤ y ≤ 5 S₁: boundary of the closed box, -2 ≤x≤ 2,-2 ≤ y ≤ 2,-2 ≤z≤2 S₂: boundary of the closed box, 1 ≤ x ≤ 2, 3 ≤ y ≤ 4,5 ≤z ≤6 S3: the sphere, x² + y² + z² = 4 S4: the sphere, (x - 5)2 + y² + z² = 1 S5: the sphere, x² + y² + z² = 9 Assume that all the curves above are oriented counterclockwise in R2, and all the surfaces are oriented outward in R³. (A) ₁ <-y, x>. dr (B) ₂ <-y, x> ||²||² dr (C) √₂ < x,y > dr Value Brief Justification
C₁: closed circle, x² + y² = 9 C₂: closed circle, (x - 2)² + y² = 1 C3: closed circle, x² + y² = 4 C4: boundary of the closed box, -1 ≤ x ≤ 3, -1 ≤ y ≤ 5 S₁: boundary of the closed box, -2 ≤x≤ 2,-2 ≤ y ≤ 2,-2 ≤z≤2 S₂: boundary of the closed box, 1 ≤ x ≤ 2, 3 ≤ y ≤ 4,5 ≤z ≤6 S3: the sphere, x² + y² + z² = 4 S4: the sphere, (x - 5)2 + y² + z² = 1 S5: the sphere, x² + y² + z² = 9 Assume that all the curves above are oriented counterclockwise in R2, and all the surfaces are oriented outward in R³. (A) ₁ <-y, x>. dr (B) ₂ <-y, x> ||²||² dr (C) √₂ < x,y > dr Value Brief Justification
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:C₁: closed circle, x² + y² = 9
C₂: closed circle, (x - 2)² + y² = 1
C3: closed circle, x² + y² = 4
C4: boundary of the closed box, -1 ≤ x ≤ 3, -1 ≤ y ≤5
S₁: boundary of the closed box, -2 ≤ x ≤ 2, -2 ≤ y ≤ 2,-2 ≤z ≤ 2
S₂: boundary of the closed box, 1 ≤ x ≤ 2, 3 ≤ y ≤ 4,5 ≤ z ≤ 6
S3: the sphere, x² + y² + z² = 4
S4: the sphere, (x - 5)² + y² + z² = 1
S5: the sphere, x² + y² + z² = 9
Assume that all the curves above are oriented counterclockwise in R2, and all the surfaces are oriented outward in R³.
(A) S₂ <-y,x>. dř
(B) Sc₂ ||||²
(C) √₂ < x,y>. dr
(D) SC3
<-y, x>. dr
(E) SCA
<-y, x>
||||²
(1) SS₂
(F) SS₂ 11711³3
(J) SS5
<-y, x>. dr
||||²
7
(G) SS₂ 11711³
(H) S₂ · dÃ
||7||3
dÃ
7 dẢ
..
||||³
dÃ
dr
dÃ
(K) curl grad f(x, y, z)
(L) V. V x F(x, y, z)
Value
Brief Justification
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