Explanation Given: The given surface is x 2 + z 2 e y − x = 13 . Given point P = ( 2 , 3 , 3 e ) Formula used: Equation of tangent plane of a surface f ( x , y , z ) = k at point P ( x 0 , y 0 , z 0 ) is given by f x ( x 0 , y 0 , z 0 ) ( x − x 0 ) + f y ( x 0 , y 0 , z 0 ) ( y − y 0 ) + f z ( x 0 , y 0 , z 0 ) ( z − z 0 ) = 0 Calculation: Consider the given surface x 2 + z 2 e y − x = 13 . f ( x , y , z ) = x 2 + z 2 e y − x − 13 ...... (1) Consider the point P = ( 2 , 3 , 3 e ) x 0 = 2 , y 0 = 3 , z 0 = 3 e Differentiate equation (1) partially with respect to x . f x ( x , y , z ) = 2 x + z 2 ( − 1 ) e y − x = 2 x − z 2 e y − x So, f x ( 2 , 3 , 3 e ) = 2 ( 2 ) − ( 3 e ) 2 e 3 − 2 = 4 − 9 e e = 4 − 9 = − 5 Differentiate equation (1) partially with respect to y

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Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 14.5, Problem 48E

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An equation of the tangent plane to the given surface at the point P(2,3,3e).

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Chapter 14.5, Problem 47E

Chapter 14.5, Problem 49E

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Chapter 14 Solutions

Calculus: Early Transcendentals

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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An equation of the tangent plane to the given surface at the point P ( 2 , 3 , 3 e ) .

Solution Summary: The author calculates an equation of the tangent plane to the given surface at the point P(2,3,3sqrte).

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To find:

An equation of the tangent plane to the given surface at the point P(2,3,3e).

Want to see the full answer?

Chapter 14 Solutions

An equation of the tangent plane to the given surface at the point P ( 2 , 3 , 3 e ) .

Solution Summary: The author calculates an equation of the tangent plane to the given surface at the point P(2,3,3sqrte).

Videos

To find: An equation of the tangent plane to the given surface at the point P(2,3,3e).

Want to see the full answer?

Chapter 14 Solutions

To find:

An equation of the tangent plane to the given surface at the point P(2,3,3e).