v = (2x² – y² +4)i+(5y+3x – 6)j . Consider two closed paths starting (and ending) at a dock located at (-1,0): (1i) path 1: the triangle from (-1,0) to (2,0) to (0,2) and back to (-1,0). (ii) path 2: the circle of radius 1 centered at (0,0), traversed counter-clockwise; (ii) path 2: the circle of radius 1 centered at (0,0), traversed counter-clockwise; Which path would cause a rower to give more effort (i.e., produce a larger hindrance)? Is vector (velocity) field is conservative, I.e., is there a function f(x, y) such that Vƒ = v?
v = (2x² – y² +4)i+(5y+3x – 6)j . Consider two closed paths starting (and ending) at a dock located at (-1,0): (1i) path 1: the triangle from (-1,0) to (2,0) to (0,2) and back to (-1,0). (ii) path 2: the circle of radius 1 centered at (0,0), traversed counter-clockwise; (ii) path 2: the circle of radius 1 centered at (0,0), traversed counter-clockwise; Which path would cause a rower to give more effort (i.e., produce a larger hindrance)? Is vector (velocity) field is conservative, I.e., is there a function f(x, y) such that Vƒ = v?
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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Transcribed Image Text:v = (2x2 – y² + 4)i+ (5y + 3x – 6)j .
Consider two closed paths starting (and ending) at a dock located at (-1,0):
(i) path 1: the triangle from (-1,0) to (2,0) to (0,2) and back to (-1,0).
(ii) path 2: the circle of radius 1 centered at (0,0), traversed counter-clockwise;
(ii) path 2: the circle of radius 1 centered at (0,0), traversed counter-clockwise;
Which path would cause a rower to give more effort (i.e., produce a larger hindrance)?
Is vector (velocity) field is conservative, I.e., is there a function f(x, y) such that Vf = v ?
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