Let F be a continuous and differentiable vector field. Suppose, for every value of r, the total flux Fout of a sphere of radius r centered at point P is given by 8r*- 3r3. a. Estimate the divergence of the field at point P (Div F(P)) using a sphere of radius 0.2 centered at P. You do not need to simplify your answer.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 78E
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8. Let F be a continuous and differentiable vector field. Suppose, for every value of r, the
total flux Fout of a sphere of radius r centered at point P is given by 8r-3r3.
Estimate the divergence of the field at point P (Div F(P)) using a sphere of
radius 0.2 centered at P. You do not need to simplify your answer.
b. Find an even better estimate of Div F(P).
Transcribed Image Text:8. Let F be a continuous and differentiable vector field. Suppose, for every value of r, the total flux Fout of a sphere of radius r centered at point P is given by 8r-3r3. Estimate the divergence of the field at point P (Div F(P)) using a sphere of radius 0.2 centered at P. You do not need to simplify your answer. b. Find an even better estimate of Div F(P).
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