Explanation Given information: f ( x , y , z ) = x y / z 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 , z ) = x y / z So, f ( x , y , z ) at ( 2 , 1 , 2 ) f ( 2 , 1 , 2 ) = ( 2 ) ( 1 ) 2 = 1 ... ( 1 ) Differentiating f ( x , y , z ) with respect to x we get, ∂ f ∂ x = ∂ ∂ x x y z ⇒ ∂ f ∂ x = y z ∂ ∂ x x ⇒ ∂ f ∂ x = y z So, f x ( x , y , z ) = y z Hence f x ( x , y , z ) at ( 2 , 1 , 2 ) f x ( 2 , 1 , 2 ) = 1 2 ... ( 2 ) Differentiating f ( x , y , z ) with respect to y we get, ∂ f ∂ y = ∂ ∂ y x y z ⇒ ∂ f ∂ y = x z ∂ ∂ y y ⇒ ∂ f ∂ y = x z f y ( x , y , z ) = x z So, f y ( 2 , 1 , 2 ) = 2 2 = 1 Hence f y ( x , y , z ) at ( 2 , 1 , 2 ) f y ( 2 , 1 , 2 ) = 2 2 = 1 ... ( 3 ) Differentiating f ( x , y , z ) with respect to z we get, ∂ f ∂ z = ∂ ∂ z x y z ⇒ ∂ f ∂ z = x y ∂ ∂ z 1 z = x y ∂ ∂ z z − 1 ⇒ ∂ f ∂ z = x y ( − 1 z 2 ) ⇒ ∂ f ∂ z = − x y z 2 So, f z ( x , y , z ) = − x y z 2 Hence f z ( x , y , z ) at ( 2 , 1 , 2 ) f z ( 2 , 1 , 2 ) = − ( 2 ) ( 1 ) ( 2 ) 2 = − 1 2

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

4th Edition

ISBN: 9781319057664

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 22E

To determine

Tofind:

linearization of f(x,y,z)=xy/z centered at (2,1,2), we have estimate f(2.05,0.9,2.01) and compare the value obtained from calculator.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 21E

Chapter 14.4, Problem 23E

Students have asked these similar questions

a is done please show b

A homeware company has been approached to manufacture a cake tin in the shape of a "ghost" from the Pac-Man video game to celebrate the 45th Anniversary of the games launch. The base of the cake tin has a characteristic dimension / and is illustrated in Figure 1 below, you should assume the top and bottom of the shape can be represented by semi-circles. The vertical sides of the cake tin have a height of h. As the company's resident mathematician, you need to find the values of r and h that minimise the internal surface area of the cake tin given that the volume of the tin is Vfixed- 2r Figure 1 - Plan view of the "ghost" cake tin base. (a) Show that the Volume (V) of the cake tin as a function of r and his 2(+1)²h V = 2

15. Please solve this and show each and every step please. PLEASE no chatgpt can I have a real person solve it please!! I am stuck. I am doing pratice problems and I do not even know where to start with this. The question is Please compute the indicated functional value.

Chapter 14 Solutions

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

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 ) = x y / z centered at ( 2 , 1 , 2 ) , we have estimate f ( 2.05 , 0.9 , 2.01 ) and compare the value obtained from calculator.

Solution Summary: The author compares the linearization of f(x,y,z)=xy/z with the value obtained from calculator.

Concept explainers

Videos

Tofind:

linearization of f(x,y,z)=xy/z centered at (2,1,2), we have estimate f(2.05,0.9,2.01) and compare the value obtained from calculator.

Want to see the full answer?

Chapter 14 Solutions

Tofind: linearization of f ( x , y , z ) = x y / z centered at ( 2 , 1 , 2 ) , we have estimate f ( 2.05 , 0.9 , 2.01 ) and compare the value obtained from calculator.

Solution Summary: The author compares the linearization of f(x,y,z)=xy/z with the value obtained from calculator.

Concept explainers

Videos

Tofind: linearization of f(x,y,z)=xy/z centered at (2,1,2), we have estimate f(2.05,0.9,2.01) and compare the value obtained from calculator.

Want to see the full answer?

Chapter 14 Solutions

Tofind:

linearization of f(x,y,z)=xy/z centered at (2,1,2), we have estimate f(2.05,0.9,2.01) and compare the value obtained from calculator.