Explanation Given: The surface is given by f ( x , y ) = 2 x − 3 y + 12 , above the region R , represented by the limit shown R = { ( x , y ) : x 2 + y 2 ≤ 9 } Formula used: The surface area can be calculated of the region R by, S = ∬ R 1 + [ f x ( x , y ) ] 2 + [ f y ( x , y ) ] 2 d A Differentiation formula d d x ( x n ) = n x n − 1 , d d x ( constant ) = 0 , The equation of circle x 2 + y 2 = r 2 , where r is the radius. Calculation: The function given is f ( x , y ) = 2 x − 3 y + 12 . Now partially differentiating it with respect to x , use d d x ( x n ) = n x n − 1 , d d x ( constant ) = 0 f x ( x , y ) = d d x ( 2 x − 3 y + 12 ) = 2 x 1 − 1 + 0 + 0 = 2 Now, with respect to y f y ( x , y ) = d d y ( 2 x − 3 y + 12 ) = 0 − 3 y 1 − 1 + 0 = − 3 Substitute in theformula S = ∬ R 1 + [ f x ( x , y ) ] 2 + [ f y ( x , y ) ] 2 d A

11th Edition

ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

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Chapter 14.5, Problem 6E

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To calculate: The area of the surface given by z=f(x,y)=2x−3y+12 which lies above the region R, represented by the limit shown R={(x,y): x2+y2≤9}

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Chapter 14.5, Problem 5E

Chapter 14.5, Problem 7E

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The area of the surface given by z = f ( x , y ) = 2 x − 3 y + 12 which lies above the region R , represented by the limit shown R = { ( x , y ) : x 2 + y 2 ≤ 9 }

Solution Summary: The author calculates the area of the surface by z=f(x,y)=2x-3y+12, above the region R.

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To calculate: The area of the surface given by z=f(x,y)=2x−3y+12 which lies above the region R, represented by the limit shown R={(x,y): x2+y2≤9}

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Chapter 14 Solutions