   Chapter 15.9, Problem 8E

Chapter
Section
Textbook Problem

Find the image of the set S under the given transformation.8. S is the square bounded by the lines u = 0, u = 1, v = 0, v = 1; x = v, y = u(1 + v2)

To determine

To find: The image R of the region S by using transformation.

Explanation

Given:

The squared region S={(u,v)|0u1,0v1} and x=v , y=u(1+v2)

Calculation:

From the given condition,

x=v (1)

y=u(1+v2) (2)

Solving the equations (1) and (2) as follows,

Substitute (1) in (2),

y=u(1+v2)y=u(1+x2)

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