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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 curl F and div F if F(x, y, z) = e-x sin y i + e-y sin z j + e-z sin x k

To determine

To Find: Thecurl F if F(x,y,z)=exsinyi+eysinzj+ezsinxk and thediv F if F(x,y,z)=exsinyi+eysinzj+ezsinxk .

Explanation

Given data:

F(x,y,z)=exsinyi+eysinzj+ezsinxk

Formula used:

Write the expression for curlF .

curlF=|ijkxyzPQR| (1)

Write the expression for divF .

divF=Px+Qy+Rz (2)

Write the required differentiation formula.

ddxex=ex

Consider the expression as follows.

F(x,y,z)=exsinyi+eysinzj+ezsinxk (3)

Write the expression for F(x,y,z) .

F(x,y,z)=Pi+Qj+Rk (4)

Compare equation (4) and (2).

P=exsinyQ=eysinzR=ezsinx

Substitute exsiny for P , eysinz for Q and ezsinx for R in equation (1),

curlF=|ijkxyzexsinyeysinzezsinx|={i[(ezsinx)y(eysinz)z]j[(ezsinx

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Chapter 16 Solutions

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Sect-16.1 P-11ESect-16.1 P-12ESect-16.1 P-13ESect-16.1 P-14ESect-16.1 P-15ESect-16.1 P-16ESect-16.1 P-17ESect-16.1 P-18ESect-16.1 P-21ESect-16.1 P-22ESect-16.1 P-23ESect-16.1 P-24ESect-16.1 P-25ESect-16.1 P-26ESect-16.1 P-29ESect-16.1 P-30ESect-16.1 P-31ESect-16.1 P-32ESect-16.1 P-33ESect-16.1 P-34ESect-16.1 P-35ESect-16.1 P-36ESect-16.2 P-1ESect-16.2 P-2ESect-16.2 P-3ESect-16.2 P-4ESect-16.2 P-5ESect-16.2 P-6ESect-16.2 P-7ESect-16.2 P-8ESect-16.2 P-9ESect-16.2 P-10ESect-16.2 P-11ESect-16.2 P-12ESect-16.2 P-13ESect-16.2 P-14ESect-16.2 P-15ESect-16.2 P-16ESect-16.2 P-17ESect-16.2 P-18ESect-16.2 P-19ESect-16.2 P-20ESect-16.2 P-21ESect-16.2 P-22ESect-16.2 P-23ESect-16.2 P-24ESect-16.2 P-25ESect-16.2 P-26ESect-16.2 P-31ESect-16.2 P-32ESect-16.2 P-33ESect-16.2 P-34ESect-16.2 P-35ESect-16.2 P-36ESect-16.2 P-37ESect-16.2 P-38ESect-16.2 P-39ESect-16.2 P-40ESect-16.2 P-41ESect-16.2 P-42ESect-16.2 P-43ESect-16.2 P-44ESect-16.2 P-45ESect-16.2 P-46ESect-16.2 P-47ESect-16.2 P-48ESect-16.2 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