Explanation Given information: The equation ∂ z ∂ x = − F x F z , ∂ z ∂ y = − F y F z Formula used: when x, y and z are related by an equation F ( x , y , z ) = 0 , ( ∂ z ∂ x ) y means same as ( ∂ z ∂ x ) and we have an equation which gives ∂ z ∂ x = − F x F z , ∂ z ∂ y = − F y F z Calculation: To prove the cyclic relation ( ∂ z ∂ x ) y ( ∂ x ∂ y ) z ( ∂ y ∂ z ) x = − 1 First from the equation ∂ z ∂ x = − F x F z , ∂ z ∂ y = − F y F z , we get ∂ z ∂ x = − F x F z , & To determine (b) To prove the cyclic relation ( ∂ z ∂ x ) y ( ∂ x ∂ y ) z ( ∂ y ∂ z ) x = − 1 When, F ( x , y , z ) = x + y + z = 0 To determine (c) To prove the cyclic relation ( ∂ T ∂ P ) P ( ∂ P ∂ V ) T ( ∂ V ∂ T ) P = − 1 For variables P, V& T in the ideal gas law P V − n R T = 0

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

See similar textbooks

Videos

Question

Chapter 14.6, Problem 42E

To determine

(a)

To prove the cyclic relation (∂z∂x)y(∂x∂y)z(∂y∂z)x=−1

With the use of equation ∂z∂x=−FxFz,∂z∂y=−FyFz

To determine

(b)

To prove the cyclic relation (∂z∂x)y(∂x∂y)z(∂y∂z)x=−1

When, F(x,y,z)=x+y+z=0

To determine

(c)

To prove the cyclic relation (∂T∂P)P(∂P∂V)T(∂V∂T)P=−1

For variables P, V& T in the ideal gas law PV−nRT=0

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.6, Problem 41E

Chapter 14.6, Problem 43E

Students have asked these similar questions

Only 100% sure experts solve it correct complete solutions ok

rmine the immediate settlement for points A and B shown in figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth of foundation (DF-0), thickness of layer below footing (H)=20m. 4m B 2m 2m A 2m + 2m 4m

sy = f(x) + + + + + + + + + X 3 4 5 7 8 9 The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem and the Mean Value Theorem for f on the closed interval [0, 9] ? (A A B B C D

Chapter 14 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

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.

(a) To prove the cyclic relation ( ∂ z ∂ x ) y ( ∂ x ∂ y ) z ( ∂ y ∂ z ) x = − 1 With the use of equation ∂ z ∂ x = − F x F z , ∂ z ∂ y = − F y F z

Solution Summary: The author explains how to prove the cyclic relation with the equation partial x=f_x, y, and z.

Videos

(a)

To prove the cyclic relation (∂z∂x)y(∂x∂y)z(∂y∂z)x=−1

With the use of equation ∂z∂x=−FxFz,∂z∂y=−FyFz

(b)

To prove the cyclic relation (∂z∂x)y(∂x∂y)z(∂y∂z)x=−1

When, F(x,y,z)=x+y+z=0

(c)

To prove the cyclic relation (∂T∂P)P(∂P∂V)T(∂V∂T)P=−1

For variables P, V& T in the ideal gas law PV−nRT=0

Want to see the full answer?

Chapter 14 Solutions

(a) To prove the cyclic relation ( ∂ z ∂ x ) y ( ∂ x ∂ y ) z ( ∂ y ∂ z ) x = − 1 With the use of equation ∂ z ∂ x = − F x F z , ∂ z ∂ y = − F y F z

Solution Summary: The author explains how to prove the cyclic relation with the equation partial x=f_x, y, and z.

Videos

(a) To prove the cyclic relation (∂z∂x)y(∂x∂y)z(∂y∂z)x=−1 With the use of equation ∂z∂x=−FxFz,∂z∂y=−FyFz

(b) To prove the cyclic relation (∂z∂x)y(∂x∂y)z(∂y∂z)x=−1 When, F(x,y,z)=x+y+z=0

(c) To prove the cyclic relation (∂T∂P)P(∂P∂V)T(∂V∂T)P=−1 For variables P, V& T in the ideal gas law PV−nRT=0

Want to see the full answer?

Chapter 14 Solutions

(a)

To prove the cyclic relation (∂z∂x)y(∂x∂y)z(∂y∂z)x=−1

With the use of equation ∂z∂x=−FxFz,∂z∂y=−FyFz

(b)

To prove the cyclic relation (∂z∂x)y(∂x∂y)z(∂y∂z)x=−1

When, F(x,y,z)=x+y+z=0

(c)

To prove the cyclic relation (∂T∂P)P(∂P∂V)T(∂V∂T)P=−1

For variables P, V& T in the ideal gas law PV−nRT=0