Let C be a simple closed curve in the xy-plane such that the point (1, -1) is not in C, and let R be the region bounded by C. Denote by n the outward pointing unit normal vector of C. Consider the function = ½ ln ((x − 1)² + (y + 1)²) on R²\{(1, −1)}, and let F = Vo. 1. Calculate F and V F on R2\{(1, −1)}. • 2. Assume that (1, -1) is not in R. Calculate ( F.nds. 3. Assume that (1, -1) is in the interior of R. Calculate f F.nds. [Notation: In w is the natural logarithmic function for w > 0.]
Let C be a simple closed curve in the xy-plane such that the point (1, -1) is not in C, and let R be the region bounded by C. Denote by n the outward pointing unit normal vector of C. Consider the function = ½ ln ((x − 1)² + (y + 1)²) on R²\{(1, −1)}, and let F = Vo. 1. Calculate F and V F on R2\{(1, −1)}. • 2. Assume that (1, -1) is not in R. Calculate ( F.nds. 3. Assume that (1, -1) is in the interior of R. Calculate f F.nds. [Notation: In w is the natural logarithmic function for w > 0.]
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
Question
![Let C be a simple closed curve in the xy-plane such that the point (1, -1) is not in C,
and let R be the region bounded by C. Denote by n the outward pointing unit normal
vector of C. Consider the function = ½ ln ((x − 1)² + (y + 1)²) on R²\{(1, −1)}, and
let F = Vo.
1. Calculate F and V F on R2\{(1, −1)}.
•
2. Assume that (1, -1) is not in R. Calculate ( F.nds.
3. Assume that (1, -1) is in the interior of R. Calculate f F.nds.
[Notation: In w is the natural logarithmic function for w > 0.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc77acd82-6ee8-4fa1-94f2-256b23fe8b4f%2F1526f9fe-dc62-44b2-9770-2f2b3b0a8c5e%2Fenfv28s_processed.png&w=3840&q=75)
Transcribed Image Text:Let C be a simple closed curve in the xy-plane such that the point (1, -1) is not in C,
and let R be the region bounded by C. Denote by n the outward pointing unit normal
vector of C. Consider the function = ½ ln ((x − 1)² + (y + 1)²) on R²\{(1, −1)}, and
let F = Vo.
1. Calculate F and V F on R2\{(1, −1)}.
•
2. Assume that (1, -1) is not in R. Calculate ( F.nds.
3. Assume that (1, -1) is in the interior of R. Calculate f F.nds.
[Notation: In w is the natural logarithmic function for w > 0.]
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