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Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516

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BuyFindarrow_forward

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
ISBN: 9781337552516
Textbook Problem

Determine whether the vector field is conservative. If it is, find a potential function for the vector field.

F ( x , y ) = ( ln y + 2 ) i ^ + x y j ^ .

To determine

Whether the vector field is conservative F(x,y) = (lny+2)i^+xyj^.. If it is, find a potentialfunction for the vector field.

Explanation

Given: The function F(x,y) = (lny+2)i^+xyj^.

A vector field F(x,y) = Mi^+Nj^ is said to be conservative if and only if

My=Nx, where M and N are differentiable functions.

Here, M=siny

Now, partial differentiating both sides with respect to ‘y’

=>My=y(lny+2)

=(ylny+y2)

=1y

and, N=xcosy

Now, partial differentiating both sides with respect to ‘x’

=>Nx=x(xy)

=1yx(x)

=1y

Clearly, My=Nx

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Chapter 15 Solutions

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P-11ESect-15.8 P-12ESect-15.8 P-13ESect-15.8 P-14ESect-15.8 P-15ESect-15.8 P-16ESect-15.8 P-17ESect-15.8 P-18ESect-15.8 P-19ESect-15.8 P-20ESect-15.8 P-21ECh-15 P-1RECh-15 P-2RECh-15 P-3RECh-15 P-4RECh-15 P-5RECh-15 P-6RECh-15 P-7RECh-15 P-8RECh-15 P-9RECh-15 P-10RECh-15 P-11RECh-15 P-12RECh-15 P-13RECh-15 P-14RECh-15 P-15RECh-15 P-16RECh-15 P-17RECh-15 P-18RECh-15 P-19RECh-15 P-20RECh-15 P-21RECh-15 P-22RECh-15 P-23RECh-15 P-24RECh-15 P-25RECh-15 P-26RECh-15 P-27RECh-15 P-28RECh-15 P-29RECh-15 P-30RECh-15 P-31RECh-15 P-32RECh-15 P-33RECh-15 P-34RECh-15 P-35RECh-15 P-36RECh-15 P-37RECh-15 P-38RECh-15 P-39RECh-15 P-40RECh-15 P-41RECh-15 P-42RECh-15 P-43RECh-15 P-44RECh-15 P-45RECh-15 P-46RECh-15 P-47RECh-15 P-48RECh-15 P-49RECh-15 P-50RECh-15 P-51RECh-15 P-52RECh-15 P-53RECh-15 P-54RECh-15 P-55RECh-15 P-56RECh-15 P-57RECh-15 P-58RECh-15 P-59RECh-15 P-60RECh-15 P-61RECh-15 P-62RECh-15 P-63RECh-15 P-64RECh-15 P-65RECh-15 P-66RECh-15 P-67RECh-15 P-68RECh-15 P-69RECh-15 P-70RECh-15 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