Explanation Given information: f ( x , y , z ) = z x + y Concept used: From the liner approximation, L ( x , y , z ) = f ( a , b , c ) + f x ( a , b , c ) ( x − a ) + f y ( a , b , c ) ( y − b ) + f z ( a , b , c ) ( z − c ) Calculation: Consider, f ( x , y , c ) = z x + y So, f ( x , y , z ) at ( 8 , 4 , 5 ) f ( 8 , 4 , 5 ) = ( 5 ) 8 + 4 = 5 12 ... ( 1 ) Differentiating f ( x , y , z ) with respect to x we get, ∂ f ∂ x = ∂ ∂ x z x + y ⇒ ∂ f ∂ x = z ∂ ∂ x x + y ⇒ ∂ f ∂ x = z ( 1 2 x + y ) ⇒ ∂ f ∂ x = z 2 x + y So, f x ( x , y , z ) = z 2 x + y Hence f x ( x , y , z ) at ( 8 , 4 , 5 ) f x ( 8 , 4 , 5 ) = 5 2 8 + 4 = 5 2 12 ... ( 2 ) Differentiating f ( x , y , z ) with respect to y we get, ∂ f ∂ y = ∂ ∂ y z x + y ⇒ ∂ f ∂ y = z ∂ ∂ y x + y ⇒ ∂ f ∂ y = z ( 1 2 x + y ) ⇒ ∂ f ∂ y = z 2 x + y So, f y ( x , y , z ) = z 2 x + y Hence f y ( x , y , z ) at ( 8 , 4 , 5 ) f y ( 8 , 4 , 5 ) = 5 2 8 + 4 = 5 2 12 ..

4th Edition

ISBN: 9781319308858

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

Videos

Question

Chapter 14.4, Problem 21E

To determine

Tofind:

linearization of f(x,y,z)=zx+y centered at (8,4,5)

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 20E

Chapter 14.4, Problem 22E

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.

Tofind: linearization of f ( x , y , z ) = z x + y centered at ( 8 , 4 , 5 )

Solution Summary: The author explains how the linearization of f(x,y,z) is centered at

Concept explainers

Videos

Tofind:

linearization of f(x,y,z)=zx+y centered at (8,4,5)

Want to see the full answer?

Chapter 14 Solutions

Tofind: linearization of f ( x , y , z ) = z x + y centered at ( 8 , 4 , 5 )

Solution Summary: The author explains how the linearization of f(x,y,z) is centered at

Concept explainers

Videos

Tofind: linearization of f(x,y,z)=zx+y centered at (8,4,5)

Want to see the full answer?

Chapter 14 Solutions

Tofind:

linearization of f(x,y,z)=zx+y centered at (8,4,5)