Explanation Given: The mapping G ( u , v ) = ( u v , u 2 − v 2 ) Calculation: Since ( x , y ) = G ( u , v ) = ( u v , u 2 − v 2 ) . Therefore, x = u v and y = u 2 − v 2 . Let u = c ,we get x = c v v = c x Now , y = c 2 − v 2 . Substituting v = c x , we get y = c 2 − ( c x ) 2 y = c 2 − c 2 x 2 y = c 2 ( 1 − 1 x 2 ) Hence, Image of the line u = c in x y -plane is y = c 2 ( 1 − 1 x 2 ) Now, we shall describe the image of the line v = c in x y plane...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 16.6, Problem 2E

To determine

To describe:

The images of the line $u = c and v = c$ [in the form $y = f (x)$ ] under the mapping $G (u, v) = (\frac{u}{v}, u^{2} - v^{2})$ .

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Chapter 16.6, Problem 1E

Chapter 16.6, Problem 3E

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Chapter 16 Solutions

CALCULUS (CLOTH)

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The images of the line u = c and v = c [in the form y = f ( x ) ] under the mapping G ( u , v ) = ( u v , u 2 − v 2 ) .

Solution Summary: The author explains how to describe the lines u = c and v in x y plane under the mapping G.

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To describe:

The images of the line $u = c and v = c$ [in the form $y = f (x)$ ] under the mapping $G (u, v) = (\frac{u}{v}, u^{2} - v^{2})$ .

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Chapter 16 Solutions

The images of the line u = c and v = c [in the form y = f ( x ) ] under the mapping G ( u , v ) = ( u v , u 2 − v 2 ) .

Solution Summary: The author explains how to describe the lines u = c and v in x y plane under the mapping G.

Concept explainers

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To describe: The images of the line u=c and v=c[in the form y=f(x)] under the mapping G(u,v)=(uv,u2−v2).

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Chapter 16 Solutions

To describe:

The images of the line $u = c and v = c$ [in the form $y = f (x)$ ] under the mapping $G (u, v) = (\frac{u}{v}, u^{2} - v^{2})$ .