1. Consider the function: -y F(x,y) = ² + y²¹ 2² + y²/ Preform the following tasks: (a) Compute the curl of F. (b) Compute fF-dr Where C is the circle of radius 1 centered at the origin oriented counterclockwise. (c) Determine whether F conservative.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Consider the function:
-y
F(x,y) = ² + y²¹ 2² + y²/
Preform the following tasks:
(a) Compute the curl of F.
(b) Compute fF-dr Where C is the circle of radius 1 centered at the origin oriented counterclockwise.
(c) Determine whether F conservative.
(d) Determine whether there is a conservative function G: R³ R³ defined everywhere except (0,0,0)
with continuous partial derivatives so that for all (x, y) = (0,0) we have:
G(1, y,0) =
2+2.0)
y
2
\x² + y²¹ x² + y²
Transcribed Image Text:1. Consider the function: -y F(x,y) = ² + y²¹ 2² + y²/ Preform the following tasks: (a) Compute the curl of F. (b) Compute fF-dr Where C is the circle of radius 1 centered at the origin oriented counterclockwise. (c) Determine whether F conservative. (d) Determine whether there is a conservative function G: R³ R³ defined everywhere except (0,0,0) with continuous partial derivatives so that for all (x, y) = (0,0) we have: G(1, y,0) = 2+2.0) y 2 \x² + y²¹ x² + y²
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