Consider the vector fieldF(x, y, z) = (ycosh x + ze*, sinh x – 3z³, e* – 9yz²)-a. Find the divergence of F at the point (0,3,1).b. Show that is conservative on R' without finding its potential.

If F→=Fxi⏞+Fyj⏞+Fzk⏞, then (a) ∇→·F→=∂Fx∂x+∂Fy∂y+∂Fz∂z and (b) F→ is conservative if ∇→×F→=0, where…

Consider the vector field F(x, y, z) = (ycosh x + ze*, sinh x – 3z³, e* – 9yz?) %3D a. Find the divergence of F at the point (0,3,1). b. Show that F is conservative on R3 without finding its potential.

Consider the vector field F(x, y, z) = (ycosh x + ze, sinh x – 3z³, e – 9yz?) %3D a. Find the divergence of F at the point (0,3,1). b. Show that F is conservative on R3 without finding its potential.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter8: Central-force Motion

Section: Chapter Questions

Problem 8.18P

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Consider the vector field
F(x, y, z) = (ycosh x + ze*, sinh x – 3z³, e* – 9yz²)
-
a. Find the divergence of F at the point (0,3,1).
b. Show that is conservative on R' without finding its potential.

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