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(1) Let F(x, y) = (2y³/2, 3x√√y). (a) Show that F is a conservative vector field. (b) Find a potential function for F. That is, find f so that F = Vƒ. (c) Find the work done by the force field F in moving an object from the point (1, 1) to the point (2,4). Note: the work integral is path independent, so use the Fundamental Theorem of Line Integrals.

(1) Let F(x, y) = (2y³/2, 3x√√y). (a) Show that F is a conservative vector field. (b) Find a potential function for F. That is, find f so that F = Vƒ. (c) Find the work done by the force field F in moving an object from the point (1, 1) to the point (2,4). Note: the work integral is path independent, so use the Fundamental Theorem of Line Integrals.

Advanced Engineering Mathematics
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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(1) Let F(x, y) = (2y³/2, 3x√√y). (a) Show that F is a conservative vector field. (b) Find a potential function for F. That is, find f so that F = Vf. (c) Find the work done by the force field ♬ in moving an object from the point (1, 1) to the point (2,4). Note: the work integral is path independent, so use the Fundamental Theorem of Line Integrals.
Transcribed Image Text:(1) Let F(x, y) = (2y³/2, 3x√√y). (a) Show that F is a conservative vector field. (b) Find a potential function for F. That is, find f so that F = Vf. (c) Find the work done by the force field ♬ in moving an object from the point (1, 1) to the point (2,4). Note: the work integral is path independent, so use the Fundamental Theorem of Line Integrals.
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