Explanation Given: Equation of surface f ( x , y ) = x 2 + y 2 + sin x y Concept Used: Gradient of a function f ( x , y ) at a point P ( x 0 , y 0 ) is: ∇ f = f x ( x 0 , y 0 ) i + f y ( x 0 , y 0 ) j The equation of tangent plane to a surface S with equation z = f ( x , y ) at point P ( x 0 , y 0 , z 0 ) is z − z 0 = f x ( x 0 , y 0 ) ( x − x 0 ) + f y ( x 0 , y 0 ) ( y − y 0 ) And its standard form is written as A x + B y + C z + D = 0 Calculation: To find the standard form of equation of the tangent plane to the surface f ( x , y ) = x 2 + y 2 + sin x y at point P 0 ( 0 , 2 , 4 ) As the equation of the tangent plane to a surface S with equation z = f ( x , y ) at point P ( x 0 , y 0 , z 0 ) is z − z 0 = f x ( x 0 , y 0 ) ( x − x 0 ) + f y ( x 0 , y 0 ) ( y − y 0 ) Thus, first find the value of f x ( 0 , 2 ) , and f y ( 0 , 2 ) as f x

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 11.4, Problem 5PS

To determine

To find the standard form of equation of the tangent plane to the surface

f(x,y)=x2+y2+sinxy at point P0(0,2,4) .

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Chapter 11.4, Problem 4PS

Chapter 11.4, Problem 6PS

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To find the standard form of equation of the tangent plane to the surface f ( x , y ) = x 2 + y 2 + sin x y at point P 0 ( 0 , 2 , 4 ) .

Solution Summary: The author explains how to find the standard form of equation of the tangent plane to the surface.

Videos

To find the standard form of equation of the tangent plane to the surface

f(x,y)=x2+y2+sinxy at point P0(0,2,4) .

Want to see the full answer?

Chapter 11 Solutions

To find the standard form of equation of the tangent plane to the surface f ( x , y ) = x 2 + y 2 + sin x y at point P 0 ( 0 , 2 , 4 ) .

Solution Summary: The author explains how to find the standard form of equation of the tangent plane to the surface.

Videos

To find the standard form of equation of the tangent plane to the surface f(x,y)=x2+y2+sinxy at point P0(0,2,4) .

Want to see the full answer?

Chapter 11 Solutions

To find the standard form of equation of the tangent plane to the surface

f(x,y)=x2+y2+sinxy at point P0(0,2,4) .