   Chapter 14.8, Problem 12E Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
ISBN: 9781285774770

Solutions

Chapter
Section Calculus: Early Transcendental Fun...

6th Edition
Ron Larson + 1 other
ISBN: 9781285774770
Textbook Problem

Using a TransformationIn Exercises 11-14, sketch the image S in the uv -plane of the region R in the xy -plane using the given transformations. x = 1 3 ( u − v ) y = 1 3 ( 2 v + u ) To determine

To graph: The image S in the uv-plane, of the region R in the xy-plane, using the given transformations x=13(vu) and y=13(2v+u).

Explanation

Given: The transformation equations x=13(vu)

y=13(2v+u)

The given rectangle is shown below.

For the graph refer to the question.

Graph: Find u and v in terms of x and y using the given transformation equation.

x=13(vu)(1)y=13(2v+u)(2)

(1)+(2) givesv=x+y...(3)

Substitute the value of v in (1)

3x=x+yuu=y2x

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