Use the definition of the divergence to show that div(c, F, + c2F;) = c, div(F,) + cz div(F,) for all constants c1, c2 € R and for all vector fields F, F : D → R³ that are differentiable. This property may be summarized by saying that the divergence is linear.
Use the definition of the divergence to show that div(c, F, + c2F;) = c, div(F,) + cz div(F,) for all constants c1, c2 € R and for all vector fields F, F : D → R³ that are differentiable. This property may be summarized by saying that the divergence is linear.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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Would like some clarity on how to solve the following divergence problem
![Use the definition of the divergence to show that
div(c, F, + c,F,) = cq div(F) + cz div(F,)
for all constants c1, c2 € R and for all vector fields F,F, : D → R³
that are differentiable. This property may be summarized by saying
that the divergence is linear.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca156d3a-526a-4574-9756-4d8e4fb28ac7%2F4bd85238-c0eb-42a5-9ba4-492713e86d02%2Fnaixurd_processed.png&w=3840&q=75)
Transcribed Image Text:Use the definition of the divergence to show that
div(c, F, + c,F,) = cq div(F) + cz div(F,)
for all constants c1, c2 € R and for all vector fields F,F, : D → R³
that are differentiable. This property may be summarized by saying
that the divergence is linear.
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