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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

Find (a) the curl and (b) the divergence of the vector field.

6. F(x, y, z) = ln(2y + 3z) i + ln(x + 3z) j + ln(x + 2y) k

(a)

To determine

To find: The curl F.

Explanation

Given data:

F(x,y,z)=ln(2y+3z)i+ln(x+3z)j+ln(x+2y)k .

Formula used:

Consider the standard equation of an curl F for F=Pi+Qj+Rk

curlF=|ijkxyzPQR| (1)

Substitute ln(2y+3z) for P , ln(x+3z) for Q and ln(x+2y) for R in equation (1),

curlF=|ijkxyzln(2y+3z)ln(x+3z)ln(x+2y)|={[y(ln(x+2y))z(ln(x+3z))]i[x(ln(x+2y))z(ln(2y+3z))]j+[x(ln(x+3

(b)

To determine

To find: The divergence of the vector field.

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Chapter 16 Solutions

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