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

4th Edition

ISBN: 9781319308858

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Videos

Question

Chapter 14.5, Problem 48E

To determine

To find:

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.5, Problem 47E

Chapter 14.5, Problem 49E

Students have asked these similar questions

Two cables tied together at C are loaded as shown. Given: Q = 130 lb. 8 30° C B Q 3 4 Draw the free-body diagram needed to determine the range of values of P for which both cables remain taut.

Cable AB is 103 ft long and the tension in the cable is 3900 lb. 56 ft A 50° 20° B x C Identify the angles 0.0, and 8, that define the direction of force. 1 By N 2 Match each of the options above to the items below. 142.1° 57.1° 73.3° 3 8.

In the given figure, P = 51 lb . 65° C 25° 35° 75 lb P Determine the corresponding magnitude of the resultant. The corresponding magnitude of the resultant is| lb.

Chapter 14 Solutions

CALCULUS:EARLY TRANS.(LL)-W/ACCESS

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

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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

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).